Alzheimer\'s disease (AD) is a challenging neurodegenerative condition, necessitating early diagnosis and intervention. This research leverages machine learning (ML) and graph theory metrics, derived from resting-state functional magnetic resonance imaging (rs-fMRI) data to predict AD. Using Southwest University Adult Lifespan Dataset (SALD, age 21-76 years) and the Open Access Series of Imaging Studies (OASIS, age 64-95 years) dataset, containing 112 participants, various ML models were developed for the purpose of AD prediction. The study identifies key features for a comprehensive understanding of brain network topology and functional connectivity in AD. Through a 5-fold cross-validation, all models demonstrate substantial predictive capabilities (accuracy in 82-92% range), with the support vector machine model standing out as the best having an accuracy of 92%. Present study suggests that top 13 regions, identified based on most important discriminating features, have lost significant connections with thalamus. The functional connection strengths were consistently declined for substantia nigra, pars reticulata, substantia nigra, pars compacta, and nucleus accumbens among AD subjects as compared to healthy adults and aging individuals. The present finding corroborate with the earlier studies, employing various neuroimagining techniques. This research signifies the translational potential of a comprehensive approach integrating ML, graph theory and rs-fMRI analysis in AD prediction, offering potential biomarker for more accurate diagnostics and early prediction of AD.

Phase transitions are typically quantified using order parameters, such as crystal lattice distances and radial distribution functions, which can identify subtle changes in crystalline materials or high-contrast phases with large structural differences. However, the identification of phases with high complexity, multiscale organization and of complex patterns during the structural fluctuations preceding phase transitions, which are essential for understanding the system pathways between phases, is challenging for those traditional analyses. Here, it is shown that for two model systems- thermotropic liquid crystals and a lyotropic water/surfactant mixtures-graph theoretical (GT) descriptors can successfully identify complex phases combining molecular and nanoscale levels of organization that are hard to characterize with traditional methodologies. Furthermore, the GT descriptors also reveal the pathways between the different phases. Specifically, centrality parameters and node-based fractal dimension quantify the system behavior preceding the transitions, capturing fluctuation-induced breakup of aggregates and their long-range cooperative interactions. GT parameterization can be generalized for a wide range of chemical systems and be instrumental for the growth mechanisms of complex nanostructures.

In this study, we propose a method for navigating the choice of treatment for stress urinary incontinence (SUI) and urgency urinary incontinence (UUI) using graph theory in discrete mathematics. Our previous study accumulated data from 150 patients who underwent tension-free vaginal tape (TVT), transobturator tape (TOT), and vaginal non-ablation Erbium YAG laser (VEL) surgeries between 2014 and 2016. Network diagrams were created using this data. The treatments TVT, TOT, and VEL, along with patient characteristics (1-hour pad test: 1-hrPadTest, Overactive Bladder Symptom Score: OABSS), were represented as nodes and edges in the network diagram. We then employed a heuristic function to select the optimal treatment method for the patients with SUI and UUI. This process enables medical professionals to easily navigate the data for patients with both SUI and UUI concerns by calculating the shortest path connecting the 1-hrPadTest and OABSS. These results, which are consistent with those of previous studies, suggest that VEL is the optimal treatment. Unlike previous studies that employed statistical knowledge that is challenging for patients to understand, our study aids patients in visually comprehending and developing a customized treatment plan. This approach introduces a novel perspective for clinical decision-making in the treatment of urinary incontinence. To the best of our knowledge, this is the first study to apply discrete mathematics to patient decision-making for urinary incontinence treatment.

This case report describes the treatment selection process for a 36-year-old woman with stress urinary incontinence (SUI) and an overactive bladder (OAB) who desired pregnancy. The patient had comorbidities of hypertension and type 2 diabetes, which required consideration to improve her quality of life and reproductive health. A recently developed decision support tool using a discrete mathematical approach was used to select a treatment method tailored to the patient\'s individual situation. The analysis determined that vaginal erbium laser (VEL) treatment (Renovalase SP Dynamis Fotona d.o.o, Ljubljana, Slovenia) was the most suitable for this patient. VEL treatment significantly improved both SUI and OAB and changing antihypertensive medication eliminated nocturia. This case suggests the potential application of graph theory in treatment selection for SUI patients.

Multiple sclerosis (MS) is a neuroinflammatory and neurodegenerative disease of the central nervous system, commonly featuring disability and cognitive impairment. The pathologic hallmark of MS lies in demyelination and hence impaired structural and functional neuronal pathways. Recent studies have shown that MS shows extensive structural disconnection of key network hub areas like the thalamus, combined with a functional network reorganization that can mostly be related to poorer clinical functioning. As MS can, therefore, be considered a network disorder, this review outlines recent innovations in the field of network neuroscience in MS.

OBJECTIVE: To determine whether individuals with subjective cognitive decline (SCD) have changes in whole-brain network characteristics and intracerebral node characteristics in the structural network, and whether there is a difference between SCD with and without Apolipoprotein E4 (APOEε4).
METHODS: This cross-sectional study included 36 individuals without SCD without APOEε4 (healthy control, HC group), 21 individuals with SCD with APOEε4 (APOEε4+ group), and 33 individuals with SCD without APOEε4 (APOEε4- group). The white matter structural network was constructed using the fractional anisotropy (FA) based deterministic fiber tracking method. Graph theory was used to analyze the whole-brain network characteristics and intracerebral node characteristics of the three groups.
RESULTS: Regarding the whole-brain network characteristics, all three groups exhibited small-worldness in their structural networks. The clustering coefficient (Cp) and local efficiency (Eloc) in the APOEε4+ and APOEε4- groups were significantly lower than in the HC group (p < 0.05), but no significant difference in Cp or Eloc was observed between the APOEε4+ and APOEε4- groups. Regarding intracerebral node characteristics, there were significant differences in some brain regions, mainly the default mode network (DMN), the occipital lobe, the temporal lobe, and subcortical regions. The change in intracerebral node characteristics was different between the APOEε4+ group and the APOEε4- group.
CONCLUSIONS: Individuals with SCD demonstrate changes in whole-brain network characteristics and intracerebral node characteristics in the structural network. Moreover, differences exist between APOEε4+ and APOEε4- individuals.

This article introduces a novel index aimed at uncovering specific brain connectivity patterns associated with Alzheimer\'s disease (AD), defined according to neuropsychological patterns.
Electroencephalographic (EEG) recordings of 370 people, including 170 healthy subjects and 200 mild-AD patients, were acquired in different clinical centres using different acquisition equipment by harmonising acquisition settings. The study employed a new derived Small World (SW) index, SWcomb, that serves as a comprehensive metric designed to integrate the seven SW parameters, computed across the typical EEG frequency bands. The objective is to create a unified index that effectively distinguishes individuals with a neuropsychological pattern compatible with AD from healthy ones.
Results showed that the healthy group exhibited the lowest SWcomb values, while the AD group displayed the highest SWcomb ones.
These findings suggest that SWcomb index represents an easy-to-perform, low-cost, widely available and non-invasive biomarker for distinguishing between healthy individuals and AD patients.

Autism spectrum disorder (ASD) is a heterogeneous, early-onset neurodevelopmental condition characterized by persistent impairments in social interaction and communication. This study aims to delineate ASD subtypes based on individual gray matter brain networks and provide new insights from a graph theory perspective. In this study, we extracted and normalized single-subject gray matter networks and calculated each network\'s topological properties. The heterogeneity through discriminative analysis (HYDRA) method was utilized to subtype all patients based on network properties. Next, we explored the differences among ASD subtypes in terms of network properties and clinical measures. Our investigation identified three distinct ASD subtypes. In the case-control study, these subtypes exhibited significant differences, particularly in the precentral gyrus, lingual gyrus, and middle frontal gyrus. In the case analysis, significant differences in global and nodal properties were observed between any two subtypes. Clinically, subtype 1 showed lower VIQ and PIQ compared to subtype 3, but exhibited higher scores in ADOS-Communication and ADOS-Total compared to subtype 2. The results highlight the distinct brain network properties and behaviors among different subtypes of male patients with ASD, providing valuable insights into the neural mechanisms underlying ASD heterogeneity.

The concept of functional localization within the brain and the associated risk of resecting these areas during removal of infiltrating tumors, such as diffuse gliomas, are well established in neurosurgery. Global efficiency (GE) is a graph theory concept that can be used to simulate connectome disruption following tumor resection. Structural connectivity graphs were created from diffusion tractography obtained from the brains of 80 healthy adults. These graphs were then used to simulate parcellation resection in every gross anatomical region of the cerebrum by identifying every possible combination of adjacent nodes in a graph and then measuring the drop in GE following nodal deletion. Progressive removal of brain parcellations led to patterns of GE decline that were reasonably predictable but had inter-subject differences. Additionally, as expected, there were deletion of some nodes that were worse than others. However, in each lobe examined in every subject, some deletion combinations were worse for GE than removing a greater number of nodes in a different region of the brain. Among certain patients, patterns of common nodes which exhibited worst GE upon removal were identified as \"connectotypes\". Given some evidence in the literature linking GE to certain aspects of neuro-cognitive abilities, investigating these connectotypes could potentially mitigate the impact of brain surgery on cognition.

BACKGROUND: Although reducing meat consumption is becoming increasingly popular in Western countries, such a transition to a sustainable diet can pose some nutritional risks.
OBJECTIVE: We aim to analyze the pathways for reaching a low-meat healthy diet and the changes in other food categories needed to rapidly decrease total red meat consumption.
METHODS: We used a recently developed method based on graph theory to represent all possible pathways of stepwise changes that avoid nutritional deficiencies toward a target healthy diet. Initial and target diets were defined as the daily consumption of 33 food groups. For each sex, three initial diets were taken from the French representative survey INCA3 as the mean observed diet and low (first quintile) and high (fifth quintile) meat consumption. Target diets were identified using multi-criteria optimization to minimize the long-term health risk of chronic diseases while ensuring nutritional adequacy. The Dijkstra algorithm was used to identify the optimal pathways between the initial and target diets, with the aim of reducing meat consumption as quickly as possible and thus minimizing long-term health risks.
RESULTS: Unprocessed red meat was easily minimized in the first steps of the pathways regardless of sex and initial level of meat consumption. However, processed meat could only be decreased later and required prior changes such as increases in fruit, vegetables, and oily fish. During total red meat minimization in females, securing adequate intakes of bioavailable iron had the most substantial impact on the other dietary changes needed.
CONCLUSIONS: Immediate reduction of red meat consumption is possible on the pathway to a healthy diet that avoids any nutrient deficiency. However, early increases in fruit, vegetables, and fish are required before minimizing total red meat early in the diet.