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  • A dissociation between primary motor cortex reorganization and correla

    A dissociation between primary motor cortex reorganization and correla

    Ingrid Galvis,1– 3 Timo Siepmann,3,4 Arturo Tamayo,3,5 Mary Pat Harnegie,6 Felipe Fregni1,7

    1Principles and Practice of Clinical Research (PPCR) Program, ECPE, Harvard T.H. Chan School of Public Health, Boston, MA, USA; 2Department of Radiology, Columbia University Irving Medical Center, New York, NY, USA; 3Division of Health Care Sciences, Dresden International University, Dresden, Germany; 4Department of Neurology, Medical Faculty and University Hospital Carl Gustav Carus, Technische Universität Dresden, Dresden, Germany; 5Rady Faculty of Health Sciences University Manitoba, Division Neurology, Winnipeg, Canada; 6Cleveland Clinic Floyd D. Loop Alumni Library, Cleveland, OH, USA; 7Spaulding Neuromodulation Center, Spaulding Rehabilitation Hospital, Harvard Medical School, Boston, MA, USA

    Correspondence: Ingrid Galvis, Principles and Practice of Clinical Research (PPCR) Program, ECPE, Harvard T.H. Chan School of Public Health, Boston, MA, USA, Email [email protected]

    Background: Phantom limb pain (PLP) constitutes a diagnostic and therapeutic challenge with an unknown pathophysiology that likely comprises a combination of cerebral, spinal, and peripheral nervous system pathways. A novel therapeutic field in chronic pain targets cortical areas as treatment foci for neuropathic pain. One studied target in phantom limb pain is the primary motor cortex (M1). Given some promising results of noninvasive brain stimulation to reduce PLP, understanding further the role of M1 in the mechanisms of PLP would provide important future insights to further develop this therapeutic target.
    Objective: To synthesize neuroimaging evidence on M1 reorganization in PLP and evaluate its association with pain intensity.
    Methods: Six databases (Ovid MEDLINE, Cochrane Library, CINAHL, Scopus, Web of Science and EMBASE) were searched.
    Results: Of the 2582 articles, 13 articles met our criteria and were included. Evidence demonstrated cortical reorganization in the contralateral M1, characterized by increased activation and maintained functional representation of the absent limb, lasting decades post-amputation. Patients with PLP showed significant activation in M1 and the somatosensory cortex during phantom limb movements, alongside reduced interhemispheric functional connectivity. However, results regarding the relationship between M1 reorganization and PLP intensity were inconsistent.
    Conclusion: M1 cortical reorganization plays a substantial role in PLP mechanisms, making it a viable therapeutic target. The inconsistent correlation between M1 activity and PLP severity highlights the complexity of PLP pathophysiology. Future research should standardize imaging protocols, control for confounding variables, and investigate interactions between M1 and other brain regions to improve therapeutic approaches.

    Keywords: phantom limb pain, motor cortex, motor cortex representation, brain activation

    Introduction

    Phantom limb pain (PLP) belongs to a group of neuropathic pain syndromes and is characterized by the perception of pain in a missing limb or following partial or complete deafferentation.1,2 The incidence of PLP ranges from 42.2 to 78.8%, with a reported prevalence of 45–85%. PLP onset can begin immediately or many years after amputation, occurring in 82.7% of cases within the first 12 months.2–5 In most cases, PLP subsides over time regardless of the cause of amputation, but it persists for several years in 5–10% of cases.6,7

    Despite the high incidence in amputees and impact on their quality of life,8,9 PLP remains one of the most challenging chronic pain syndromes to treat, often responding poorly to conventional therapies.1,2,10–12 Although central and peripheral factors have been implicated in the development of PLP, the former is believed to be the major contributor. It has been proposed that the phenomenon is initiated by changes arising in the periphery that alter the afferent input into the brain and spinal cord.1,3,10,13 In that way, the region that represents the missing limb in the primary somatosensory cortex (S1) becomes deprived of its primary input, resulting in functional changes in the gray and white matter, prominently in the primary sensory (S1) and motor (M1) cortices.14–18

    Neuroimaging techniques such as fMRI have thus been employed to investigate these neural alterations and guide rehabilitative strategies for PLP. fMRI has proven valuable for evaluating cortical reorganization, somatotopic representation changes, task-related activation, and treatment-related neural responses.19,20 For instance, when amputees with PLP attempt to move their phantom limbs, activation in the corresponding sensorimotor areas appears in fMRI, and this activation is similar to real executed movements in able-bodied subjects.19 Significant task-related activation in the superior temporal gyrus, medial temporal gyrus, and M1 contralateral to the executed movement has been documented in other studies.

    Furthermore, greater dependence on the intact limb has been associated with decreased white matter degeneration, improved limb representation, and cortical expansion of S1 cortex into the deprived cortex.13 It has also been proposed that brain functional network recovery occurs through progressive restoration of functional connectivity between subcortical and cortical regions, particularly involving the supplementary motor area (SMA) and the contralateral S1M1.21,22

    Despite previous reviews addressing the phantom limb pain mechanisms broadly or focusing on the therapeutic interventions, the precise role of primary motor cortex (M1) reorganization in PLP perception and intensity remains unclear.23 Neuroimaging studies have reported inconsistent findings—some showing positive associations between M1 activity and pain intensity, while others show null or contradictory results. Moreover, understanding M1 involvement is clinically relevant, as this area is targeted by rehabilitation strategies such as motor imagery, mirror therapy, and non-invasive brain stimulation, which aim to reverse maladaptive cortical changes and alleviate pain. This systematic review synthesizes the available neuroimaging evidence on M1 reorganization in PLP, with an emphasis on its relationship to pain intensity and its implications for therapy.

    Materials and Methods

    This review was conducted with the PRISMA 2020 statement (Page MJ, McKenzie JE, Bossuyt PM, et al, 2020), and an a priori protocol was registered with PROSPERO (CRD42022383423).

    Search Strategy

    We applied a search strategy developed in collaboration with an experienced librarian (MH) in Ovid MEDLINE, Cochrane Library, CINAHL, Scopus, Web of Science and EMBASE. The search was performed from each dataset’s inception until March 2023 by using controlled vocabulary, supplemented with keywords related to phantom limp pain and neuroimaging techniques. There was no language restriction placed on the search. No additional filters (eg, publication year) were set. A manual search was also conducted to find other potential articles based on references identified in the individual articles. Our full search strategy is available in the Supplemental Digital content-Search strategies.

    Eligibility Criteria

    We included original articles and case reports that had interventions with positive or negative outcomes in the primary motor cortex by using neuroimaging techniques in adults with a limb amputation and suffering from PLP. Outcomes expected: (1) structural changes in M1. (2) increased, decreased, or absence of neuronal activation in the M1 after imagined phantom limb movements or TDCs. There was no language restriction placed on the search.

    Exclusion Criteria

    The following criteria were used to exclude studies: (1) wrong patient population: studies that included adults with any limb amputation, but without PLP. (2) wrong intervention: studies that did not use neuroimaging techniques in patients with PLP (3) wrong outcomes: studies that included amputees with PLP who underwent any of the neuroimaging modalities but did not report either positive or negative outcomes in the primary motor cortex. (4) wrong study design: (a) animal studies; (b) review articles; (c) letters to the editor; (d) editorials. Duplicated studies were also removed.

    Data Collection and Management

    Two independent reviewers (IG, EL) screened the abstracts and assessed them for inclusion and exclusion criteria. Duplicated records were removed. Then, full texts were read and assessed for eligibility. Any discrepancies were discussed between the two reviewers initially and if no agreement was reached, this was solved by another reviewer (HA). Extraction of relevant results was checked (10% of the time) by a second reviewer (HA). Due to the heterogeneity in study designs and outcome reporting, a meta-analysis was not feasible. Instead, a narrative synthesis was conducted. Findings were grouped and interpreted based on task type (eg, motor execution vs imagery) and reported associations between M1 activity and phantom limb pain intensity.

    Protocol Deviations

    Following PROSPERO registration (CRD42022383423), a number of adjustments were made to improve the comprehensiveness of the review. These included (1) expanding the databases searched to include CINAHL and Scopus, (2) removal of the language restriction to capture a broader range of studies, and (3) inclusion of both case-control and cross-sectional studies. These changes were implemented to capture a more representative and updated evidence base and are transparently reported here.

    Risk of Bias Assessment

    One reviewer (HA) independently assessed the risk of bias of the studies according to the Newcastle -Ottawa quality assessment scale,24 and the results were displayed using the “robvis” package.25 Three domains were evaluated: subject selection, comparability, and the assessment of the exposure. The evaluation was reported as “low”, “some concerns” or “high”, as summarized in Figure 1.

    Figure 1 Literature search flow-chart.

    Results

    Studies Retrieval

    The results of the search strategy are summarized in Figure 2 as PRISMA statement flow diagram. The literature search resulted in 1494 articles after duplicates were removed. Based on titles and abstracts screening, 1196 articles were excluded. The remaining 298 articles underwent full-text screening to identify studies reporting M1 findings in PLP patients using neuroimaging techniques. Although our initial search included a broad range of neuroimaging modalities, only studies employing functional MRI (fMRI) met our criteria for inclusion. In this phase, 281 articles were excluded as they did not report M1 findings, did not include PLP patients, or had an inappropriate study design (eg, review articles). Therefore, 13 articles were included: 1 case report, 10 case-controls studies, and 2 cross-sectional studies.

    Figure 2 Risk of bias assessment.

    Overall Characteristics

    Among the patient’s characteristics, the predominant cause of amputation was trauma. Most of the studies involved upper-limb amputees, and only four studies included lower-limb amputees. The right upper limb was the most affected, and only 5 studies mentioned the use of prostheses. The time since amputation ranged from 1.5 years to 21.3 years (mean 14.27 years). fMRI was the most common neuroimaging used to evaluate cortical reorganization after performing tasks, imaginary/mental training, or undergoing neurostimulation. Most of the studies included healthy patients without amputation as controls. Only one study used subjects as their own control, comparing against the participants’ ipsilateral hemisphere to the amputation.

    One study evaluated transcranial direct current stimulation over the primary sensorimotor missing cortex (S1/M1) to alleviate PLP. Eleven studies assessed cortical reorganization in M1/S1 in imagined phantom limb movements, mental imagery, and mirror therapy. The characteristics of the included articles are summarized in Table 1. Study heterogeneity prevented data pooling.

    Table 1 Characteristic of Included Studies

    Clinical Findings-Role of the Primary Motor Cortex in Imaginary Movements

    Reorganization in M1/S1 contralateral to the amputation side has been suggested to be the main neural correlate of PLP. Supporting this idea, Lotze et al27 studied upper limb amputees and found that only patients with PLP presented a shift of the lip representation into the deafferented primary motor and somatosensory hand areas during lip movements and imagined movements of the phantom hand. Moreover, the displacement of the lip representation in the primary motor and somatosensory cortex was positively correlated to the intensity of PLP (Table 2).

    Table 2 Summary of Functional MRI Findings Reported in Studies of Phantom Limb Pain

    Contrary to the shift in motor cortex representation mentioned previously, Raffin et al31 and Kikkert et al35 found that maintained representation of the missing limb in the primary somatosensory cortex seems to be associated with chronic PLP. They consider that PLP is associated with the preservation of the grey matter volume in the cortical area of the missing limb. Additionally, Makin et al32 found that individuals suffering more from PLP have a greater reduction in interhemispheric functional connectivity, which could explain the decrease in callosal white-matter fractional anisotropy in lower limb amputees documented by Simões et al.38 Therefore, multiple factors interact to preserve the local structural and functional representations, but, at the same time, disrupt the interhemispheric connectivity.

    In addition, most of the studies found that during the imagination of moving the phantom hand, a significant activation in the contralateral primary motor (M1) and somatosensory cortices was present compared with imagination hand movements in the control groups. However, only the patients with PLP during the imagined movement of the phantom activated the neighboring face cortical area and had increased activation in the M1/S1 lip area contralateral to the amputation side. Thus, the increased neuronal activation in the contralateral M1 during imaginary limb movements proves that the cortical areas of the missing limb are still functional even decades after amputation.13,39

    Likewise, the imaginary movement of the phantom limb activates cortical areas that differ from the intact limb movement. Roux et al29 found that the activation during imaginary movement in control subjects did not activate the precentral or postcentral gyri. In its place, activation was mainly in the SMA region. Supporting this idea, Romero et al40 studied lower limb amputees and found that the brain activation during the imagery movement tasks of the amputated lower limbs involves the superior temporal gyrus, contralateral M1, and contralateral SMA.

    Interestingly, activation of the basal ganglia loop was not seen during the imagery movement task of the intact toes in amputees or the healthy control group. Only during imaginary limb movements, increased activation was found in the contralateral basal ganglia at the medial globus pallidus, substantia nigra, and thalamus.40 The increased activation in the basal ganglia–thalamus–cortex pathway during imaginary movement of the phantom toes may reflect an abnormal open loop functioning of the thalamocortical system underlying the conscious awareness of the phantom phenomenon.40

    Regarding the intensity of pain in amputee patients, the contradictory results in the studies cannot provide certain evidence about the role of M1 in modulating pain. Makin et al,32 Kikkert et al,35 and Andoh et al41 found an association between the degree of activation in the contralateral M1 during phantom movement and the intensity of pain in amputees, with greater activation in individuals with a worse history of PLP. In contrast to that, Duarte et al36 found that PLP intensity is not associated with signal changes in M1 and a shift in motor cortex representation. Instead, signal changes in M1 are inversely correlated with time since amputation. Thus, longer periods of amputation lead to compensatory changes in sensory-motor areas with fewer changes in the contralateral M1. Duarte et al36 conclude that signal changes in the visual cortex seem to be more related to greater pain.

    Clinical Correlation—M1 Activation and Pain Relief

    Elimination of cortical reorganization—evidenced by reduced activation in the contralateral M1 and S1 of the missing limb—has been associated with decreased intensity and unpleasantness of chronic pain in amputees. Supporting this, Maclver et al30 studied 13 upper-limb amputees and found that after 6-week training in mental imagery, patients presented a significant reduction in both the intensity and unpleasantness of persistent pain and its exacerbations, accompanied by a reversal of cortical reorganization.30 Before training, cortical activation during lip pursuing extended abnormally from the lip area into the deafferented hand region of M1 and S1 a pattern that correlated with pain severity.

    Foell et al33 investigating the effects of mental imagery on PLP found similar changes.33 The study showed that the pain relief induced by mirror therapy is associated by a reversion of dysfunctional cortical reorganization, but mainly in S1. As PLP decreased, the representation of the missing limb in the somatosensory cortices become similar, possibly returning to their normal state. However, for the motor cortex, no connection was found. Instead, pain reduction after mirror training was related to a decrease in activity in the inferior parietal cortex (IPC), an area connected to the interpretation of sensory information, and pain generation. That might suggest that the ability to relate the mirror image to one’s phantom influence the treatment effectiveness to alleviate pain.42 They also found no significant correlation between time since amputation and the treatment effects of mirror therapy.

    Some evidence suggests that other pain-related areas are involved in the physiopathology of PLP. Kikkert et al35 found that using task-concurrent NIBS stimulation in the mid and posterior insula and S2 reduced activity in the S1/M1 of the missing hand cortex. The reduced activity in M1/S1 was correlated with PLP relief. However, this study provides additional evidence that highlights the causal role of the mid and posterior insula in alleviating PLP, possibly through S1/M1 modulation.

    Raffin et al31 found that the amount of ipsilateral activity in the former hand area (M1) while moving the intact hand is correlated with the ability to move the phantom. Therefore, these findings correlated with the studies that found the reactivation of the deprived cortex (M1) when moving the intact and phantom limbs during mirror or imagery therapy.26,28 Hence, this evidence reinforces the utility of these therapies to protect against reorganization of the motor cortex contralateral to the amputation and reduce phantom pain.

    Clinical Correlation-Control Group Findings

    Although the exact mechanisms behind the mode of action of mirror therapy (MT) are not clear, it has been proposed that there is representational restoration in the brain of the missing limb by the conjunction of visual and proprioceptive input. Foell et al33 used the hemispheres ipsilateral to the amputation as controls for the measured changes in cortical activity after 4 weeks of MT. The study found no significant association between the cortical shift in the ipsilateral S1 and M1 with treatment benefit. Therefore, any changes in the ipsilateral hemisphere after MT did not influence PLP relief. In contrast to a reduction of dysfunctional reorganization in the contralateral S1 that was correlated with pain relief.

    Discussion

    Our review highlights cortical organization at a network-level scale, with reduced interhemispheric functional connectivity of the contralateral M1 and S1.43–45 The findings in the studies suggest that cortical reorganization leads to PLP, and it is accompanied by the persistence of the missing limb’s representation. Amputees who suffer from PLP seem to have greater cortical reorganization compared to amputees without pain.46,47 The amount of cortical reorganization in some studies has been strongly related to the intensity of PLP4.45 Zhang et al20 and Lotze et al27 found that the cortical shift is positively correlated with the PLP intensity.20 In other words, PLP has a negative correlation with cortical reorganization and the reduction in pain intensity.48 In contrast, Gunduz et al46 and Pacheco et al49 did not find any correlation between motor cortex reorganization and level of pain. Pacheco et al49 conclude that the amount of cortical reorganization could be associated with the presence of pain instead of its severity.49

    Hence, neuroplasticity-based methods that strengthen the cortical representation of the phantom and decrease the cortical reorganization have been used for the relief of PLP.50–56 Among these PLP therapies, motor imagination, mirror therapy, and repetitive magnetic stimulation (rTMS) have shown inconsistent results. Repetitive magnetic stimulation (rTMS) over M1 has been revealed to temporarily alleviate the painful cramping sensation in the phantom limb and even provoke a sensation of movement.4,21,38,57–59

    M1 plays a role in alleviating pain relief in PLP patients by mechanisms that are contradictory and not well understood. As described by Duarte et al,36 the posterior M1 is linked to nonmotor regions including sensory and attentional brain areas that can suggest its modulation in pain.36 Therefore, this could explain the reversibility of neuroplastic changes in patients after transcranial direct current stimulation over the M1. In addition, since M1 is involved in the planning of action and execution of a motor task, the virtual reality mirror box (VRMB) has also been used to bring back the representation of the missing hand and reverse the maladaptive brain plasticity. In amputees, VRMB has shown significant task-related activation in the primary motor (MI) and somatosensory cortex (SI) contralateral to the executed movement.21,56 Likewise, there is increased functional connectivity between the M1 (contralateral to the executed movement) and the medial occipital cortex, bilateral precuneus, caudate, superior frontal and superior medial frontal cortices, and angular gyrus.21,60 Although similar brain areas are activated in motor imagery and execution, the degree of activation is different. For example, excitatory coupling between the thalamus and primary motor cortex is present during motor execution, but not in motor imagery.22,61

    Taken together, the findings confirm that different components of pain (cognitive, affective, and discriminative) can be assigned to different brain regions and these areas play a role in the distinctive pain experienced by each individual (see Figure 3).55 Pacheco et al49 suggested that PLP intensity may be more related to neuronal circuits associated with emotional processing.49 Therefore, the maladaptive cortical reorganization seems to activate pain circuits and the circuits related to emotional affective processing regulate the pain intensity. As described, the somatosensory cortex seems to be associated with the sensory-discriminative component, but the thalamus and limbic structures may determine their significance for the generation of affective and cognitive aspects of pain. Likewise, the insula may have a causal role (and other pain-related areas) in alleviating PLP, potentially through S1/M1 modulation.

    Figure 3 Factors determining the outcome of PLP.43

    Abbreviations: M1, Primary motor cortex; S1, Primary somatosensory cortex; PFC, Prefrontal cortex; IPC, inferior parietal cortex.

    There is also an important role of self-perception and corporeal awareness of body integrity that is optimized with a mirrored image of intact limbs.28,62 That concept is supported by the ability of the visual cortex to generate kinesthetic motor imagery of own body movement.61,63 Therefore, mirror therapy demonstrates the capacity to incorporate visual inputs in tasks by using similar approaches as motor execution (M1 activation). Moreover, the decrease of activity in the inferior parietal cortex (IPC) after mirror therapy also suggests its influence on the interpretation of sensory information and alleviation of pain.33

    Similarly, the presence of itching in PLP patients as a compensatory mechanism to decrease neuropathic pain was suggested by Duarte et al.36 They evidenced an association between the decreased activity in M1 and itching sensation compared with subjects without itching. Pain and itching have been found to partially activate the same cortical areas in healthy individuals (the anterior cingulate cortex, the anterior insula, the basal ganglia and the pre-supplementary motor area) which suggest that the two sensations may be interlinked on a neurophysiological level.64 However, only pain has been found to induce an activation of the thalamus, and being significantly correlated to pain sensation. These findings support the idea that the thalamus and S2 are important components for pain perception and demonstrate the central mechanisms of itching distinct from pain.64

    Due to the rapid appearance of symptoms in some cases after amputation, cortical reorganization has been proposed to be a result of unmasking occult synapses in the somatosensory cortex, rather than specific anatomical changes.39 A theory states that PLP may also arise from errors occurring in that cortical remapping process and leading to over-amplification of the pain experienced. This is the result of a lack of inhibitory activity in the sensory-cortical feedback pathways with a continued efferent motor cortical command. These are hypotheses and the current therapies have provided some clues about the physiopathology of PLP.

    Given the controversial findings, larger studies evaluating the neurophysiological and structural changes in patients with PLP are needed, specifically focusing on the different brain areas that interlay and interact with the primary motor cortex to modulate pain. Likewise, a challenge to PLP research begins with how PLP is quantified. Most of the PLP treatment outcomes are measured by self-report, and as mentioned previously, PLP is heterogeneous like the experience (quality, intensity, frequency, time of onset, etc) and its association with other phantom sensations. Münger et al65 found that 90% of patients with PLP experience at least 1 phantom sensation such as electric sensations, itching, and movement.65

    Therefore, if the symptoms are assessed by trained research staff instead of questionnaire-based, the risk of response bias is reduced. Consequently, an analysis of the fMRI series can provide detailed and accurate results about the precise cortical areas activated in pain. Lastly, one limitation of retrospective pain assessments before the amputation is the recall bias. Patients with chronic pain may have difficulties rating their pre-amputation pain correctly when the amputation occurred months or years previously.

    Finally, more longitudinal studies with larger sample sizes, and more homogeneous populations, considering the different factors associated with PLP are needed. The studies should include patients with low-intensity PLP or without pain as controls to assess the amount of reorganization more precisely with the presence of PLP and identify potential patients with an increased risk of developing phantom pain.

    Limitations

    This review has several limitations. First, the number of included studies was relatively small, which limits the breadth and statistical robustness of the findings. Second, there was substantial heterogeneity in study designs, participant characteristics, neuroimaging protocols, and the tasks employed (eg, motor execution vs imagery), making direct comparisons difficult. Third, the majority of research relied on self-reported, subjective measures of phantom limb pain, which are subject to recall and reporting bias. Fourth, due to the variability in outcomes and reporting, no quantitative synthesis or meta-analysis was conducted, and between-study heterogeneity was not formally assessed.

    As a result, the synthesis was descriptive and qualitative, which limits the generalizability of conclusions. Fifth, the possibility of publication bias cannot be ruled out, particularly given the limited number of studies and the tendency to publish significant findings. Finally, most included studies involved upper-limb amputees, which may limit the generalizability of the findings to lower-limb amputees or other amputation contexts. Despite these limitations, this review offers valuable insights into the role of M1 in PLP and highlights directions for future research.

    Conclusion

    This systematic review highlights the involvement of the M1 in the pathophysiology of PLP, with fMRI studies demonstrating cortical reorganization that may correlate with pain persistence or response to therapy. These findings suggest that M1 could serve as a potential target for neuromodulatory interventions. However, M1 does not operate in isolation. Several studies also reported changes in regions such as SI, SMA, and temporal gyri, indicating that PLP is mediated by a distributed cortical and subcortical network. These broader findings warrant further integration into neurorehabilitation strategies.

    Despite the progress in functional imaging, inconsistencies in study design, outcome measures, and imaging paradigms limit the comparability of existing findings. Future research should prioritize standardized imaging protocols, stratification by limb type (upper vs lower extremity), and control for key confounders such as prosthesis use, time since amputation, handedness, and pre-amputation pain history. Longitudinal studies with larger and more diverse populations will be essential to clarify causal mechanisms and support personalized therapeutic approaches. In addition, the inclusion of control groups in future studies would allow for direct comparison, thereby enhancing the interpretability and robustness of the results.

    Neuroimaging continues to offer a valuable insight into the central mechanisms underlying PLP and has the potential to guide more targeted and effective treatments as evidence accumulates.

    Acknowledgments

    We thank Dr. Hedaia Alquatani (HA) and Dr. Eddy Lincango (EL) for helping in the screening of articles and risk of bias assessment. ChatGPT-4 (OpenAI) was used to edit and refine the manuscript text. The authors reviewed and approved all content.

    Funding

    This research received no external funding.

    Disclosure

    The authors report no conflicts of interest in this work.

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    29. Roux FE, Lotterie JA, Cassol E, Lazorthes Y, Sol JC, Berry I. Cortical areas involved in virtual movement of phantom limbs: comparison with normal subjects. Neurosurgery. 2003;53(6):1342–1353. doi:10.1227/01.NEU.0000093424.71086.8F

    30. MacIver K, Lloyd DM, Kelly S, Roberts N, Nurmikko T. Phantom limb pain, cortical reorganization and the therapeutic effect of mental imagery. Brain. 2008;131(Pt 8):2181–2191. doi:10.1093/brain/awn124

    31. Raffin E, Richard N, Giraux P, Reilly KT. Primary motor cortex changes after amputation correlate with phantom limb pain and the ability to move the phantom limb. Neuroimage. 2016;130:134–144. doi:10.1016/j.neuroimage.2016.01.063

    32. Makin TR, Scholz J, Filippini N, Henderson Slater D, Tracey I, Johansen-Berg H. Phantom pain is associated with preserved structure and function in the former hand area. Nat Commun. 2013;4:1570. doi:10.1038/ncomms2571

    33. Foell J, Bekrater-Bodmann R, Diers M, Flor H. Mirror therapy for phantom limb pain: brain changes and the role of body representation. Eur J Pain. 2014;18(5):729–739. doi:10.1002/j.1532-2149.2013.00433.x

    34. Kikkert S, Mezue M, Henderson Slater D, Johansen-Berg H, Tracey I, Makin TR Motor correlates of phantom limb pain. Cortex. 2017;95:29–36. doi:10.1016/j.cortex.2017.07.015

    35. Kikkert S, Johansen-Berg H, Tracey I, Makin TR. Reaffirming the link between chronic phantom limb pain and maintained missing hand representation. Cortex. 2018;106:174–184. doi:10.1016/j.cortex.2018.05.013

    36. Duarte D, Bauer CCC, Pinto CB, et al. Cortical plasticity in phantom limb pain: a fMRI study on the neural correlates of behavioral clinical manifestations. Psychiatry Res Neuroimaging. 2020;304:111151. doi:10.1016/j.pscychresns.2020.111151

    37. Andoh J, Milde C, Diers M, et al. Assessment of cortical reorganization and preserved function in phantom limb pain: a methodological perspective. Sci Rep. 2020;10(1):11504. doi:10.1038/s41598-020-68206-9.

    38. Simões EL, Bramati I, Rodrigues E, et al. Functional expansion of sensorimotor representation and structural reorganization of callosal connections in lower limb amputees. J Neurosci. 2012;32(9):3211–3220. doi:10.1523/JNEUROSCI.4592-11.2012

    39. Makin TR, Flor H. Brain (re)organisation following amputation: implications for phantom limb pain. Neuroimage. 2020;218:116943. doi:10.1016/j.neuroimage.2020.116943

    40. Romero-Romo JI, Bauer CC, Pasaye EH, Gutiérrez RA, Favila R, Barrios FA. Abnormal functioning of the thalamocortical system underlies the conscious awareness of the phantom limb phenomenon. Neuroradiol J. 2010;23(6):671–679. doi:10.1177/197140091002300605

    41. Andoh J, Milde C, Tsao JW, Flor H. Cortical plasticity as a basis of phantom limb pain: fact or fiction? Neuroscience. 2018;387:85–91. doi:10.1016/j.neuroscience.2017.11.015

    42. Schone HR, Baker CI, Katz J, et al. Making sense of phantom limb pain. J Neurol Neurosurg Psychiatry. 2022;93(8):833–843. doi:10.1136/jnnp-2021-328428

    43. Makin TR, Filippini N, Duff EP, Henderson Slater D, Tracey I, Johansen-Berg H. Network-level reorganisation of functional connectivity following arm amputation. Neuroimage. 2015;114:217–225. doi:10.1016/j.neuroimage.2015.02.067

    44. Schwenkreis P, Witscher K, Janssen F, et al. Assessment of reorganization in the sensorimotor cortex after upper limb amputation. Clin Neurophysiol. 2001;112(4):627–635. doi:10.1016/S1388-2457(01)00486-2

    45. Wiech K, Preissl H, Birbaumer N. Neuroimaging of chronic pain: phantom limb and musculoskeletal pain. Scand J Rheumatol Suppl. 2000;113:13–18. doi:10.1080/030097400446571

    46. Gunduz ME, Pinto CB, Saleh Velez FG, et al. Motor cortex reorganization in limb amputation: a systematic review of TMS motor mapping studies. Front Neurosci. 2020;14:314. doi:10.3389/fnins.2020.00314

    47. Montoya P, Ritter K, Huse E, et al. The cortical somatotopic map and phantom phenomena in subjects with congenital limb atrophy and traumatic amputees with phantom limb pain. Eur J Neurosci. 1998;10(3):1095–1102. doi:10.1046/j.1460-9568.1998.00122.x

    48. Osumi M, Ichinose A, Sumitani M, et al. Restoring movement representation and alleviating phantom limb pain through short-term neurorehabilitation with a virtual reality system. Eur J Pain. 2017;21(1):140–147. doi:10.1002/ejp.910

    49. Pacheco-Barrios K, Pinto CB, Saleh Velez FG, et al. Structural and functional motor cortex asymmetry in unilateral lower limb amputation with phantom limb pain. Clin Neurophysiol. 2020;131(10):2375–2382. doi:10.1016/j.clinph.2020.06.024

    50. Guo X, Liu R, Lu J, et al. Alterations in brain structural connectivity after unilateral upper-limb amputation. IEEE Trans Neural Syst Rehabil Eng. 2019;27(10):2196–2204. doi:10.1109/TNSRE.2019.2936615

    51. Bao BB, Zhu HY, Wei HF, et al. Altered intra- and inter-network brain functional connectivity in upper-limb amputees revealed through independent component analysis. Neural Regen Res. 2022;17(12):2725–2729. doi:10.4103/1673-5374.339496

    52. Bogdanov S, Smith J, Frey SH. Former hand territory activity increases after amputation during intact hand movements, but is unaffected by illusory visual feedback. Neurorehabil Neural Repair. 2012;26(6):604–615. doi:10.1177/1545968311429687

    53. Ortiz-Catalan M, Guðmundsdóttir RA, Kristoffersen MB, et al. Phantom motor execution facilitated by machine learning and augmented reality as treatment for phantom limb pain: a single group, clinical trial in patients with chronic intractable phantom limb pain. Lancet. 2016;388(10062):2885–2894. doi:10.1016/S0140-6736(16)31598-7

    54. Tominaga W, Matsubayashi J, Furuya M, et al. Asymmetric activation of the primary motor cortex during observation of a mirror reflection of a hand. PLoS One. 2011;6(11):e28226. doi:10.1371/journal.pone.0028226

    55. Arena JG, Sherman RA, Bruno GM, Smith JD. The relationship between situational stress and phantom limb pain: cross-lagged correlational data from six month pain logs. J Psychosom Res. 1990;34(1):71–77. doi:10.1016/0022-3999(90)90009-S

    56. Yanagisawa T, Fukuma R, Seymour B, et al. BCI training to move a virtual hand reduces phantom limb pain: a randomized crossover trial. Neurology. 2020;95(4):e417–e426. doi:10.1212/WNL.0000000000009858

    57. Nurmikko T, MacIver K, Bresnahan R, Hird E, Nelson A, Sacco P. Motor cortex reorganization and repetitive transcranial magnetic stimulation for pain-a methodological study. Neuromodulation. 2016;19(7):669–678. doi:10.1111/ner.12444

    58. Reilly KT, Sirigu A. Motor cortex representation of the upper-limb in individuals born without a hand. PLoS One. 2011;6(4):e18100. doi:10.1371/journal.pone.0018100

    59. Roux FE, Ibarrola D, Lazorthes Y, Berry I. Chronic motor cortex stimulation for phantom limb pain: a functional magnetic resonance imaging study: technical case report. Neurosurgery. 2001;48(3):681–688. doi:10.1097/00006123-200103000-00050

    60. Bonnal J, Ozsancak C, Prieur F, Auzou P. Video mirror feedback induces more extensive brain activation compared to the mirror box: an fNIRS study in healthy adults. J Neuroeng Rehabil. 2024;21(1):78. doi:10.1186/s12984-024-01374-1

    61. Bajaj S, Butler AJ, Drake D, Dhamala M. Brain effective connectivity during motor-imagery and execution following stroke and rehabilitation. Neuroimage Clin. 2015;8:572–582. doi:10.1016/j.nicl.2015.06.006

    62. Anderson WS, Lenz FA. Review of motor and phantom-related imagery. Neuroreport. 2011;22(17):939–942. doi:10.1097/WNR.0b013e32834ca58d

    63. Roth M, Decety J, Raybaudi M, et al. Possible involvement of primary motor cortex in mentally simulated movement: a functional magnetic resonance imaging study. Neuroreport. 1996;7(7):1280–1284. doi:10.1097/00001756-199605170-00012

    64. Mochizuki H, Sadato N, Saito DN, et al. Neural correlates of perceptual difference between itching and pain: a human fMRI study. Neuroimage. 2007;36(3):706–717. doi:10.1016/j.neuroimage.2007.04.003

    65. Münger M, Pinto CB, Pacheco-Barrios K, et al. Protective and risk factors for phantom limb pain and residual limb pain severity. Pain Pract. 2020;20(6):578–587. doi:10.1111/papr.12881

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  • All four, once more? Sinner and Alcaraz target another sweep of the majors – ATP Tour

    1. All four, once more? Sinner and Alcaraz target another sweep of the majors  ATP Tour
    2. Carlos Alcaraz wins first Cincinnati Open title as Jannik Sinner retires with illness  CNN
    3. Giri Nathan DISHES On Jannik Sinner And Carlos Alcaraz In This EXCLUSIVE Interview  Defector
    4. Giri Nathan, CHANGEOVER: A Young Rivalry and a New Era of Men’s Tennis  iHeart
    5. Carlos Alcaraz and Jannik Sinner’s tennis takeover: Book excerpt from Giri Nathan’s “Changeover” – The Athletic  The New York Times

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  • PCB unveils central contracts for 2025–26, no players in category ‘A’

    PCB unveils central contracts for 2025–26, no players in category ‘A’

    The Pakistan Cricket Board (PCB) on Tuesday confirmed central contracts for 30 men’s cricketers for the 2025–26 season, with no player included in Category A this year.
    According to the PCB press release, the new contracts, which run from July 1, 2025, to June 30, 2026, divide the players equally across Categories B, C, and D, with 10 cricketers placed in each group.
    Compared to last year’s list of 27, the pool has been expanded to 30, featuring 12 new names. The fresh inclusions are Ahmed Daniyal, Faheem Ashraf, Hasan Ali, Hasan Nawaz, Hussain Talat, Khushdil Shah, Mohammad Abbas, Mohammad Haris, Mohammad Nawaz, Sahibzada Farhan, Salman Mirza, and Sufiyan Muqeem.
    Five players have been rewarded with promotions following strong displays over the past year. Abrar Ahmed, Haris Rauf, Saim Ayub, Salman Ali Agha, and Shadab Khan have all moved up from Category C to Category B.
    Meanwhile, nine players have kept their previous slots. Among them are Abdullah Shafique in Category C, Khurram Shahzad, Mohammad Abbas Afridi, and Mohammad Wasim Jnr in Category D, Noman Ali, Sajid Khan, and Saud Shakeel in Category C, while Shaheen Shah Afridi continues in Category B.
    However, eight cricketers who were part of last year’s contracts have missed out this time. Aamer Jamal, Haseebullah, Kamran Ghulam, Mir Hamza, Mohammad Ali, Mohammad Huraira, Muhammad Irfan Khan, and Usman Khan, all previously in Category D, have not been retained.

    The list of centrally contracted players for the 2025–26 season:
    Category B: Abrar Ahmed, Babar Azam, Fakhar Zaman, Haris Rauf, Hasan Ali, Mohammad Rizwan, Saim Ayub, Salman Ali Agha, Shadab Khan and Shaheen Shah Afridi.
    Category C: Abdullah Shafique, Faheem Ashraf, Hasan Nawaz, Mohammad Haris, Mohammad Nawaz, Naseem Shah, Noman Ali, Sahibzada Farhan, Sajid Khan and Saud Shakeel.
    Category D: Ahmed Daniyal, Hussain Talat, Khurram Shahzad, Khushdil Shah, Mohammad Abbas, Mohammad Abbas Afridi, Mohammad Wasim Jnr, Salman Mirza, Shan Masood and Sufiyan Muqeem.

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  • Time series forecasting of infant mortality rate in India using Bayesian ARIMA models | BMC Public Health

    Time series forecasting of infant mortality rate in India using Bayesian ARIMA models | BMC Public Health

    Some suggested ARIMA models and Bayes estimates for real-world time series data sets are numerically illustrated in this section. The example serves as a key demonstration of how our models work in finding a true state of the system by showcasing the method’s practical utility and relevance to real-life problems. In addition to the analysis, we have also mentioned the forecast for future purposes.

    Data source

    We have taken a real data set of the IMR for India over the period of 73 years from 1950 to 2023 annually. The data set is given in the form of a time series from World Population Prospects. World Population Prospects is the twenty-seventh edition of official United Nations population estimates and projections that have been prepared by the Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat. It presents population estimates from 1950 to the present for 237 countries or areas underpinned by analyses of historical demographic trends. This latest assessment considers the results of 1,758 national population censuses conducted between 1950 and 2023, as well as information from vital registration systems and 2,890 nationally representative sample surveys (UN-WPP). Table 2 shows the IMR values, and Table 3 shows the IMR growth rate in percentage.

    Table 2 Infant mortality rate in India from 1950 to 2023 (values decrease from left to right)
    Table 3 Infant mortality growth rate in India (in percentage), 1951–2023

    After understanding the dataset, we have drawn the time series plot of IMR growth rate data and differenced IMR growth rate. These plots are given in Fig. 1.

    Fig. 1

    Time series plots showing IMR growth and differenced IMR growth rate of India from 1951-2023

    After plotting the IMR growth data, it can be observed that it is not stationary (see Fig. 1a). However, after differencing it once, we obtain stationarity in Fig. 1b. This shows that we can set (d=1). The ADF test also shows that unit root is not present for the first difference. The p-value (=0.31) is also greater than 0.05.

    ACF and PACF plots for the given data

    Selecting the appropriate values for p and q is crucial in building an effective ARIMA model for a given time series [7]. To determine p and q, we have drawn the ACF and PACF plots as mentioned in Determining the order section. This plotting involves computing the autocorrelation function (ACF) and partial autocorrelation function (PACF) plots of the time series data. ACF is a plot of the correlation of a series with its own lagged values. PACF plot is a plot of the partial correlation between a series and its lagged values, regressed the values of the time series at all shorter lags. ACF and PACF plots of the data are given in Fig. 2.

    Fig. 2
    figure 2

    ACF and PACF plots of the IMR growth dataset after first differencing

    The above ACF (see in Fig. 2a) and PACF plots (see in Fig. 2b) are shown with details. Significant autocorrelation spikes at specific lags may indicate periodic behaviour or a strong dependence on past values, as seen at lag 5, which is the highest. Significant spikes at multiple lags may suggest a mix of autoregressive and moving average components, indicating a more complex time series structure in the partial autocorrelation at lags 5 and 10, respectively. Furthermore, these plots provide valuable insights into the temporal dependencies within a time series, aiding in model selection and forecasting. Using all the nearest possible combinations of AR lag, fixing the difference at one time, and other nearest lag possible combinations of MA order, we go for the likelihood estimation and Bayesian estimation as well in the next section.

    Classical analysis

    The primary aim of the study is to emphasise Bayesian analysis, a crucial aspect of establishing initial values to compute the MLE using the Newton-Raphson method. This initial value helps us to run the algorithm 3.4. In this study, the ARIMA model results from the specified combinations of (p, d, q), namely (5,1,0), (5,1,1), (5,1,2),(5,1,3),(5,1,4),(5,1,5), (0,1,5), (1,1,5), (2,1,5),(3,1,5), (4,1,5) and (5,1,5). Since we have stationarity at the first lag, we have selected d = 1. Although the ACF and PACF plots suggest a lag of 5, we are not very sure about it. Therefore, we have selected these combinations of p and q. We have computed the MLE for the mentioned models, along with their respective standard errors (SE), for the above-selected combinations of p and q in the ARIMA (pdq) model, and their AIC and BIC values. The results are shown in Table 4.

    Table 4 MLEs, SE, and model comparison (AIC and BIC) for various ARIMA(p,1,q) model configurations applied to IMR growth data

    From Table 4, it can be seen that the ARIMA models generally show consistent parameter estimates across different parameter specifications, with varying degrees of uncertainty (as indicated by the standard error, SE). Notably, the order (5,1,0) and (0,1,5) models have more stable parameter estimates with relatively lower standard errors compared to higher-order models like (5,1,3), (5,1,4), (5,1,5), where standard errors are larger, indicating less precise estimates. Additionally, the ARIMA models with moving average terms (e.g., order (5,1,1) and (5,1,2)) show slightly higher parameter variability, suggesting increased model complexity that may lead to poor precision.

    Besides classical estimates, Table 4 presents AIC and BIC values. Based on these values, we can say that ARIMA models with orders (5,1,0), (5,1,1), (0,1,5) and (1,1,5) are performing better than the others. Also, it is well known that Bayesian analysis is computationally costly, due to the need for repeated likelihood evaluations and high-dimensional sampling using Markov Chain Monte Carlo (MCMC) methods. Each iteration of the Random Walk Metropolis algorithm requires evaluating the full likelihood via the Kalman filter, which increases computational load significantly. Therefore, to ensure tractability and focus on the most promising configurations, we restrict the Bayesian analysis to four models that showed the best performance in the classical model selection phase. Therefore, we plan to perform a Bayesian analysis for these four models only. In the next subsection, we will provide the Bayesian analysis of these four models.

    Bayesian analysis

    To conduct Bayesian analysis, the initial step involves determining the prior hyperparameters. Since the Bayesian framework relies heavily on prior information, carefully selecting priors is crucial to avoid misleading results. As suggested in Prior distribution section, the most appropriate prior for both the (phi) and (theta) parameters is the Multivariate Normal (MVN) distribution. We choose the hyperparameters as follows: The MLE (hat{phi }) of ({phi }) is considered as the prior mean for the respective AR models. The diagonal elements of the prior variance-covariance matrix (Sigma) is 2(times) abs [({phi _1}), ({phi _2}),…, ({phi _5})]. The non-diagonal elements of (Sigma) are considered to be zero. In the same way, we choose the MLE and diagonal elements of the prior variance-covariance matrix for the (theta) parameter of the MA model (details mention in 3.2).

    We now proceed to run the RWM algorithm, as discussed in Random walk Metropolis (RWM) algorithm section. The proposal scale, (sigma), has been chosen in the algorithm to keep the acceptance rate optimal. The initial values of the chain are set to the corresponding MLE. The algorithm has been run for 5e5 iterations. Under the aforementioned conditions, the optimal acceptance rate ranged from (10%) to (60%), indicating a low rejection rate of the algorithm.

    Table 5 presents estimated posterior characteristics for different configurations of the models, which have been chosen according to the minimum AIC and BIC values. So, we have chosen four models of order (5,1,0). (5,1,1), (0,1,5), (1,1,5). The posterior summary includes the posterior mean, median, mode, and highest posterior density (HPD) intervals with a 0.95 probability.

    Table 5 Posterior summaries for selected ARIMA(p,1,q) models based on IMR growth data

    By varying the hyperparameter of prior distributions and comparing the resulting posterior summaries, we observed that the estimates remained largely consistent, indicating robustness of the Bayesian inference. Across the models, the parameter estimates indicate variability in both magnitude and uncertainty. In general, the fifth lag of the AR or MA terms shows relatively larger means and wider HPD intervals, suggesting a stronger or more uncertain contribution at that lag. Comparing models, the ARIMA(5,1,1) and ARIMA(1,1,5) appear to capture richer dynamics due to the inclusion of both AR and MA terms, although some parameters show wide HPD intervals, implying caution in their interpretation.

    From Fig. 3 shows the trace plots from 5e5 MCMC iterations show well-mixed, stationary chains for all five parameters, with no visible trends or drifts. The rapid fluctuations indicate low autocorrelation, suggesting good convergence and reliable posterior sampling. This analysis helps identify the most suitable model structure for forecasting while highlighting parameter uncertainty. Further details of this combination of models has been discussed in the next subsection.

    Fig. 3
    figure 3

    Trace plot of the parameters for order (5,1,1)

    Bayesian model selection

    In order to proceed with model selection, which is to make a comparison among models, and wish to know the best one among four models considered for Bayesian Analysis. We have used the AIC score, BIC score for model selection as discussed in Bayesian Model selection section. Also, K-fold cross-validation (CV) is used to assess the predictive performance of the selected models on simulated time series data. For practical compatibility, K is commonly set to 5 or 10; this study chose K = 10, following [34]. The results are shown in Table 6.

    Table 6 Model comparison based on AIC, BIC, and forecast error metrics

    The Table 6 presents a comparative analysis of four Bayesian ARIMA model configurations (5,1,0), (5,1,1), (0,1,5), and (1,1,5)—based on evaluation metrics such as AIC, BIC, MSE, RMSE, and MAE. Among them, the ARIMA(5,1,0) model demonstrates the best performance, having the lowest AIC (18.68), BIC (30.14), and the most favorable error values (MSE = 4.72, RMSE = 2.17, MAE = 1.66). To provide a more comprehensive evaluation of model performance, we also computed Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) for each selected ARIMA model. These metrics offer additional insight into forecast accuracy, with RMSE being sensitive to large errors and MAE providing a more robust view of average forecast deviations. The ARIMA(5,1,0) model outperforms the others across all four criteria—AIC, BIC, RMSE, and MAE—reinforcing its status as the most reliable model for forecasting India’s IMR growth.

    However, ARIMA(5,1,0) offers several additional advantages that justify its selection. First, it has a simpler structure with fewer parameters than ARIMA(1,1,5) or ARIMA(0,1,5), which reduces the risk of overfitting and enhances model interpretability. Second, in the Bayesian estimation process, the ARIMA(5,1,0) model demonstrated better convergence diagnostics (e.g., well-mixed trace plots and stable posterior distributions), indicating numerical stability and robustness. These practical and computational considerations, along with its marginally better predictive accuracy, make ARIMA(5,1,0) the most appropriate model for forecasting India’s infant mortality rate in this study.

    Retrospective study

    This retrospective study examines the trend in interval estimates over the period 2015 to 2023. The intervals represent credible intervals, reflecting changes observed year-over-year. By systematically analysing these intervals, the study aims to understand the longitudinal behaviour of IMR growth rate, offering insights that may support future forecasting or decision-making.

    The Table 7 presents forecasted IMR growth rates from 2015 to 2023, each accompanied by a 95% confidence interval. While the predicted values consistently show a decline in IMR growth( in %) over time, the widening confidence intervals (CI), especially in later years, indicate increasing uncertainty in the forecasts. This suggests that although the model anticipates continued improvement, the reliability of long-term predictions decreases as the forecast horizon extends.

    Table 7 Retrospective study of IMR growth rate (in %) for the period 2015 to 2023

    Again, for validating the model’s accuracy and reliability we are comparing the forecasted IMR growth rates and their confidence intervals with actual observed data is essential. It shows how well the model reflects real trends, whether its uncertainty estimates are appropriate, and helps identify over or underestimations. This comparison also supports model refinement and builds credibility, making the forecasts more meaningful for evidence-based decision-making.

    The Table 8 compares actual and forecasted IMR values from 2015 to 2023, along with the absolute error for each year. The results show that the model consistently overestimated IMR across all years, with forecasted values slightly higher than actual figures. While the forecast closely matched actual IMR in 2015 (smallest error: 0.22), the accuracy gradually declined over time, reaching the highest discrepancy in 2023 (1.51). This pattern suggests the model performs better for short-term predictions, but its accuracy diminishes as the forecast horizon extends. Overall, the model demonstrates a reasonable fit, though its tendency to over-predict should be noted for future refinement.

    Table 8 Comparison between actual historical IMR values and forecasted values during the retrospective period (2015–2023)

    Comparing predictive performance

    As the purpose of this article is to forecast the IMR growth data using a Bayesian ARIMA model. But for the simplicity of this study, we can go for the Autoregressive(AR) model to predict the same dataset. And also make a comparison of the predictive performance between the common forecasting model and the Bayesian ARIMA model. Since, AR models are ideal for small, stationary datasets, capturing temporal dependence through past values. They’re simple, interpretable, and effective for short-term forecasts, requiring no external inputs.

    Bayesian ARIMA provides probability distributions for forecasts, and also requires a more iterative process to find the estimates. Bayesian ARIMA offers enhanced precision by incorporating uncertainty and adaptability. The choice between the two depends on the complexity of the dataset and the need for probabilistic forecasting. To evaluate the comparative performance of the two models, we present Table 9, which reports the IMR values and their growth rates for the same year, along with the corresponding 95% CI for both the AR model and the Bayesian ARIMA model.

    Table 9 Comparison of predictive performance of IMR (per 1,000 live births) and growth rate data for the period of 2015 to 2023

    The Bayesian ARIMA model demonstrates superior forecasting performance compared to the AR model, as shown by significantly lower MSE values averaging 4.3 across 10 folds versus 18.5 for the AR model. Also, its ability to provide probabilistic confidence intervals enhances its reliability in uncertain environments. Compared to the AR model, Bayesian ARIMA delivers more accurate and informative forecasts, especially when accounting for uncertainty and evolving data patterns.

    Forecasting

    To fulfil the second objective of our study, we have generated forecasts for the subsequent periods based on the fitted time series model. The model captured the underlying patterns and trends in the historical data, and the forecasted values provide an estimate of the expected behaviour moving forward. The result of the point forecast for IMR and IMR growth (in %) with their respective credible interval are summarised in Table 10 for the next decade.

    Table 10 Forecast of IMR (per 1,000 live births) data for the period of 2024 to 2033

    To obtain these patterns, we initially simulated the corresponding posterior and obtained a posterior sample of size 1e5 for the ARIMA(5,1,0) model using available data values. Subsequently, we simulated predictive samples for the remaining unobserved datasets for each value in the simulated posterior sample. The predictive estimates are provided as the corresponding posterior modes based on 100 predictive samples. These samples are used to apply the Kalman filter to predict future observations by using the model’s estimated parameters and current state information.

    The forecasted IMR from 2024 to 2033 in Table 10 indicates a consistent downward trend, highlighting gradual improvements in infant mortality rates (IMR). Starting from an IMR of 25.21 in 2024, the rate steadily declines to 15.68 by 2033. The year-over-year growth rate remains negative throughout the period, with the highest reduction observed in 2033 (-5.81%). The output typically includes forecasted values along with their associated uncertainties, which helps with short-term time series prediction.

    From Fig. 4 shows that the trend is promising as this persistent decline reflects the potential impact of public health interventions, improved healthcare services, and socio-economic development. The model effectively captures this trend, offering valuable projections for health policy planning and evaluation.

    Fig. 4
    figure 4

    Forecasted IMR growth trend with credible intervals

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  • Samsung is giving away a free 65-inch TV right now — here’s how to get yours

    Samsung is giving away a free 65-inch TV right now — here’s how to get yours

    BOGO SAMSUNG TVS: Until Sept. 7, Samsung is offering a “buy one, get one free” TV deal. When you buy a Super Big Samsung TV, you’ll get a 65-inch Class UHD TV for free.


    There aren’t many deals that get the people going like a “buy one, get one free” promotion. And then when that deal includes Samsung TVs, it’s time to shut up shop for the day. We haven’t seen something this huge before (literally), so you just know that shoppers are at least going to take a look. If not just to dream.

    Until Sept. 7, Samsung is offering a “buy one, get one free” deal on some absolutely massive TVs. When you buy a Super Big Samsung TV, you’ll get a 65-inch Crystal UHD U8000F for free. What’s a Super Big Samsung TV? We’re talking about TVs of 98 inches or more.

    SEE ALSO:

    Record-low price alert: The 55-inch TCL QM6K QLED 4K TV is $350 off at Amazon

    To qualify for this bonkers BOGO deal, you’ll need to purchase one of the following models:

    To secure this deal, you’ll need to add both the Crystal UHD U8000F and qualifying TV to your cart. Samsung will then automatically apply the discount at the checkout. Interested? You might need to act fast as stock already looks limited.

    Mashable Deals

    We totally get that this deal won’t appeal to everyone. The qualifying TVs are not exactly cheap, but if you’re already in the market for something massive, you might as well double up for no extra expense.

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  • On Pixel’s big day, Samsung is offering $300 off the Galaxy Z Fold 7 foldable phone

    On Pixel’s big day, Samsung is offering $300 off the Galaxy Z Fold 7 foldable phone

    SAVE $300: As of Aug. 20, the Samsung Galaxy Z Fold 7 is on sale for $1,699.99 at Amazon. That’s a 15% saving on the list price


    Google’s Pixel 10 is taking the spotlight on Aug. 20, with an expected launch at the Made By Google 2025 event. But it’s not the only new phone making moves. Samsung has lined up a hefty $300 discount on its brand-new Galaxy Z Fold 7, giving anyone tempted by the foldable trend another reason to look around before committing.

    As of Aug. 20, the Galaxy Z Fold 7, usually priced at $1,999.99 at Amazon, is now $1,699.99. This deal is for the 256GB option, and it’s available in three colors: blue shadow, jet black, and silver shadow, all at the same low price.

    SEE ALSO:

    Samsung is giving away a free 65-inch TV right now — here’s how to get yours

    This is a fantastic phone, even without the fancy folding feature. It features a 200MP main camera powered by Samsung’s Pro-Visual Engine and an 8-inch internal screen that supports up to three windows at once — perfect for multitasking. The battery life is great, too, designed to last all day. This remains the same even with heavy usage like running multiple apps, streaming video, or gaming.

    And it uses a customized Snapdragon 8 Elite processor, designed specifically for Galaxy devices, to handle demanding tasks like streaming, editing, and multitasking smoothly. So, even if you’re on it all day using multiple apps at once, it will still run fast with no lag. On the outside, it’s built strong, made with an Armor Aluminum frame and Gorilla Glass Ceramic 2 for added durability. So if you drop your phone a lot, you’ll have extra floor protection with this smartphone.

    Mashable Deals

    Read to jump on the folding phone trend? Get this deal at Amazon.

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  • Ulanzi Studio Deck Dock D200H

    Ulanzi Studio Deck Dock D200H

    The older I’ve gotten, the more I’ve realised how convenient having studio-grade tools is as part of your workstation. Thankfully, these tools have gotten cheaper and more readily accessible over time, and they’re all vying to be the best in the market. 

    High-quality sound output is a great example of this. For sound, you can choose to have a sound card within your case, or even output to a mixer on your desk. You’ve got a plethora of options, and it doesn’t take much to get a massive boost in audio quality just by spending $40-60 more. 

    That’s not the only place that these tools have seen huge competition in. Elgato’s Stream Deck is arguably the king of this castle, and has been so for many, many years. That’s very clear in how they price it. However, like every empire, they’re constantly having to fend off the attacks by rogue competitors who want a piece of the pie, and now and again, these empires fall. 

    And that’s what Ulanzi Studio is trying to do.

    The Deck Dock D200H is a macro-key competitor to the 15-key Elgato Stream Deck. That is, if the Stream Deck were also compatible with their external USB Hub like the Stream Deck + is. Visually, both Decks are extremely similar – offering 14/15 keys on the face that are mapped via software that you run on your PC, which must be running in the background at all times to use it, and they’re both using very similar-looking software that is extremely customizable and easy to use. 

    But that’s where the similarities stop, because unlike having to spend over $200 with Elgato to get the same functionality as a Stream Deck with a USB Hub, it all comes in one $65 package. 

    The Deck Dock D200H has a USB A 3.0 and USB-C 3.0 ports on the right side, an SD and Micro SD card slot on the left side, USB-A 3.0 and USB-C 3.0 ports, and a PD100W power supply on the rear next to the PC connection port. It’s all extremely convenient, as if designed as a middle finger to Elgato’s insane broken-up and expensive product catalog. It not only saves money, but it’s a huge bonus to have one or two less USB hubs on a desk.

    However, one of the areas where Elgato is stronger is the Plugin catalog. With Elgato’s offering, you not only get a massive collection to choose from that’s almost never-ending, they’re also custom-built by multiple different creators. With Ulanzi, you’re limited to what they’ve created themselves, and that means you’re waiting on one developer to update any flagged issues. 

    One thing I don’t like about the Deck Dock D200H is how it sits on the desk. It’s as if it’s designed more for a standing desk user, since its face points upwards at a 20-30° angle. Unfortunately, they don’t provide an additional 45° stand to mount it in, and it has a habit of slipping if you try to lean it against something. If you’re like me and have information displayed on the screen, like CPU usage or are trying to navigate multiple menus, it can be inconvenient having to lean over the screen to read it. 

    Other than that, the buttons feel like a weird in-between of a membrane and scissor-switch keyboard, and need to be interacted with in the dead center for it to read your input. If you were using this as your go-to day in, day out, and you had to constantly interact with the button for it to read your input, you’d quickly get irritated.

    At the end of the day, I really like what Ulanzi has put together – but where it falls short, it falls hard. It provides a lot of usability through USB-A/C and SD card ports, but it feels inconvenient to use at times. If you can get past its faults, I don’t see why this couldn’t be a great budget option to go with.

    Review Guidelines

    75

    Ulanzi Studio Deck Dock D200H

    Good

    The Deck Dock D200H is a great all-in-one budget solution for those wanting a macro keyboard, USB hub, and Micro SD/SD card reader. Its software is extremely easy to use, extremely customizable, and works directly with the software I use daily. However, just like with every budget option, there are distinct flaws – the buttons aren’t satisfying to press, it has a habit of not reading my inputs, and it sits at a very inconvenient angle if you’re sitting at your desk.


    Pros
    • Huge amount of usability packed into one device
    • Paired with very easy-to-use software
    • Insanely affordable, especially against competitors like Elgato
    Cons
    • Sits at a weird 20-30° angle
    • Buttons aren’t satisfying to press and must be interacted with in the dead center for it to read an input
    • Animated GIFs don’t seem to work properly on the display
    • Limited plugin options via Ulanzi Studio


    This review is based on a copy provided by GamingTrend.


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  • 3D Artist Reimagines Demon Slayer’s Mitsuri Kanroji With Maya & UE5

    3D Artist Reimagines Demon Slayer’s Mitsuri Kanroji With Maya & UE5

    While the days when the Kimetsu no Yaiba, a.k.a. Demon Slayer, series was all the rage and the talk of the town within the anime/manga community have long passed, it without a doubt still stands as one of the most iconic franchises with countless fans all across the world.

    Proving that point is 3D Character Artist known as Clear777, who recently showcased a stunning 3D recreation of one of the series’ most memorable supporting characters, Mitsuri Kanroji. As the artist noted, this fan work helped them study XGen, Mari, and Unreal Engine 5, three of the key applications used to bring the model to life. In addition, they also utilized such software as ZBrush, Maya, Substance 3D Painter, Marmoset Toolbag, and Marvelous Designer.

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  • Singer Tamar Braxton says she ‘almost died’ in weekend accident

    Singer Tamar Braxton says she ‘almost died’ in weekend accident

    LOS ANGELES — Singer, actor and reality TV star Tamar Braxton said Tuesday that she “almost died” in a weekend accident that she doesn’t remember.

    “I was found in a pool of blood from my friend with a face injury,” Braxton wrote in an Instagram post. “I fractured my nose, lost some teeth and mobility.” She added, “I don’t even know what happened to me.”

    Braxton, 48, earlier in the day had posted “Thank you God for waking me up today,” in an Instagram story.

    She said she was getting calls after and was struggling to talk so she shared what had happened to her.

    The post also said “the way I look at life now is totally different. As my health is on the mend my mental journey begins… pray for me for real.”

    An email to Braxton’s manager seeking more details was not immediately answered.

    Braxton was part of a singing group with her sisters, including Toni Braxton, who went on to a major solo career.

    They and other family members appeared on the reality series “Braxton Family Values” starting in 2011, and Tamar Braxton has since appeared in spin-offs and other reality shows.

    As an actor, her recent credits include the TV series “Kingdom Business.” And she has spent much of the year on a solo singing tour.


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  • Bank Indonesia front-loads easing amid growth concerns | articles

    Bank Indonesia front-loads easing amid growth concerns | articles

    Bank Indonesia has lowered its policy rate by 25 basis points to 5.00%, marking a second consecutive surprise cut. While we had expected BI to hold off on further easing until the fourth quarter – given the recent strength in GDP and CPI data, as well as weak transmission to lending rates – the move signals BI’s increasing concern over the growth outlook.

    The decision also suggests that BI is taking advantage of periods of Indonesian rupiah (IDR) strength to ease policy without risking currency instability. Despite headline inflation ticking higher, it remains well below BI’s upper target of 3.5%, giving the central bank room to act pre-emptively to support domestic demand.

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