Exact Analysis of TTL Cache Networks: The Case of Caching Policies driven by Stopping Times

TTL caching models have recently regained significant research interest, largely due to their ability to fit popular caching policies such as LRU. This paper advances the state-of-the-art analysis of TTL-based cache networks by developing two exact methods with orthogonal generality and computational complexity. The first method generalizes existing results for line networks under renewal requests to the broad class of caching policies whereby evictions are driven by stopping times. The obtained results are further generalized, using the second method, to feedforward networks with Markov arrival processes (MAP) requests. MAPs are particularly suitable for non-line networks because they are closed not only under superposition and splitting, as known, but also under input-output caching operations as proven herein for phase-type TTL distributions. The crucial benefit of the two closure properties is that they jointly enable the first exact analysis of feedforward networks of TTL caches in great generality

The Max-Flow Min-Cut Theorem for Countable Networks

We prove a strong version of the Max-Flow Min-Cut theorem for countable networks, namely that in every such network there exist a flow and a cut that are "orthogonal" to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain infinite trails then this flow can be chosen to be mundane, i.e. to be a sum of flows along finite paths. We show that in the presence of infinite trails there may be no orthogonal pair of a cut and a mundane flow. We finally show that for locally finite networks there is an orthogonal pair of a cut and a flow that satisfies Kirchhoff's first law also for ends.Comment: 19 pages, to be published in Journal of Combinatorial Theory, Series

A meta-analytic approach to the association between inhibitory control and parent-reported behavioral adjustment in typically-developing children: Differentiating externalizing and internalizing behavior problems

Impairments in inhibitory control (IC) are traditionally seen as a vital aspect in the emergence and course of maladaptive behavior across early childhood. However, it is currently unclear whether this view applies to both the externalizing and internalizing domain of parent-reported behavioral adjustment. Furthermore, past (meta-analytic) developmental research and theory characterizing this association have largely neglected the vast heterogeneity of IC measures and conceptualizations. The present meta-analyses examined the association of IC with parent-reported externalizing (N = 3160, 21 studies) and internalizing (N = 1758, 12 studies) behavior problems, assessed with the Child Behavior Checklist (CBCL), in non-clinical populations of children aged 2-8 years. They further investigated the moderating effects of a priori IC categorization, according to a recently proposed two-factor model of IC ("Strength/Endurance" account, Simpson & Carroll, 2019). In line with previous research in the clinical domain, the current results corroborate the notion of a robust, but small association between IC and externalizing behavior problems (r = -0.11) in early childhood. However, although frequently proposed in the literature, no significant linear association could be identified with internalizing behavior problems. Furthermore, in both meta-analyses, no significant moderating effects of IC categorization could be revealed. These findings enhance our knowledge about the cognitive underpinnings of early-emerging maladaptive behavior, indicating that different subtypes of IC are statistically related with externalizing, but not internalizing behavior problems. Overall, the small association of IC ability with behavior problems in non-clinical populations provokes broader questions about the role of IC in behavioral adjustment

Pathomechanisms of mutant proteins in Charcot-Marie-Tooth disease

We review the putative functions and malfunctions of proteins encoded by genes mutated in Charcot-Marie-Tooth disease (CMT; inherited motor and sensory neuropathies) in normal and affected peripheral nerves. Some proteins implicated in demyelinating CMT, peripheral myelin protein 22, protein zero (P0), and connexin32 (Cx32/GJB1) are crucial components of myelin. Periaxin is involved in connecting myelin to the surrounding basal lamina. Early growth response 2 (EGR2) and Sox10 are transcriptional regulators of myelin genes. Mutations in the small integral membrane protein of lysosome/late endosome, the myotubularin-related protein 2 (MTMR2), and MTMR13/set-binding factor 2 are involved in vesicle and membrane transport and the regulation of protein degradation. Pathomechanisms related to alterations of these processes are a widespread phenomenon in demyelinating neuropathies because mutations of myelin components may also affect protein biosynthesis, transport, and/or degradation. Related disease mechanisms are also involved inaxonal neuropathies although there is considerably more functional heterogeneity. Some mutations, most notably in P0, GJB1, ganglioside-induced differentiation-associated protein 1 (GDAP1), neurofilament light chain (NF-L), and dynamin 2 (DNM2), can result in demyelinating or axonal neuropathies introducing additional complexity in the pathogenesis. Often, this relates to the intinate connection between Schwann cells and neurons/axons leading to axonal damage even if the mutation-caused defect is Schwann-cell-autonomous. This mechanisms is likely for P0 and Cx32 mutations and provides the basis for the unifying hypothesis that also demyelinating neuropathies develop into functional axonopathies. In GDAP1 and DNM2 mutants, both Schwann cells and axons/neurons might be directly affected. NF-L mutants have a primary neuronal defect but also cause demyelination. The major challenge ahead lies in determining the individual contributions by neurons and Schwann cells to the pathology over time and to delineate the detailed molecular functions of the proteins associated with CMT in health and diseas

The Influence of Leadership on Employees' Work‑nonwork Interface and Wellbeing: A Scoping Review

Many current working conditions are characterized by increasing blurred boundaries between work and nonwork with spillover that impact employees’ and recovery processes and wellbeing. Research, although emerging, considers these processes in the leadership-wellbeing relationship insufciently. The main aim of this study, therefore, was to enhance our understanding of the role of leadership on employee’s work-nonwork interface and wellbeing. To address these processes adequately, longitudinal research is most appropriate. To our best knowledge, no review exists that could inform longitudinal studies on the leadership-employee wellbeing relationship with a focus on spillover and recovery processes. Following the PRISMA Extension for Scoping Reviews, we apply a narrative synthesis of 21 identifed studies to organize the research landscape. We make three main contributions: First, we adopt an integrated resource-demands based process perspective and expand the leadership-employee wellbeing relationship by including spillover and recovery. Second, we map the used theoretical approaches and analyzed research gaps. Third, we ofer a list of the issues and potential remedies of applied methodologies to orient further research. Results show, that while work nonwork research is predominantly approached from a negative confict-based view, research focused more on positive than on negative leadership. We identify two broad categories of investigated mechanisms, namely bolstering/hampering mechanisms, and bufering/strengthening mechanisms. Findings also highlight the importance of personal energy resources and therefore call for more attention to afect-driven theories. The identifed predominance of the IT and healthcare sectors and of working parents warrants more representative research. We ofer recommendations to advance future research both theoretically and methodologically

The Indirect Role of Passive-Avoidant and Transformational Leadership through Job and Team Level Stressors on Workplace Cyberbullying

Research on workplace cyberbullying (WCB) is still scarce and needs verification. This study addressed the indirect influence of positive and negative leadership on WCB via perceived role stressors and negative team climate. The main goal is to test the applicability of the work environment hypothesis and job demands-resources model for WCB on a cross-sectional sample of n = 583 workers in Germany (n = 334) and Spain (n = 249). We tested multiple mediation models, and findings revealed that negative (passive-avoidant) leadership increased role and team stressors and thereby WCB exposure, whereas positive (transformational) leadership decreased the same stressors and thereby reduced WCB exposure. No cross-cultural differences were found, indicating portability of the results. This study highlights the explanatory factors for WCB at individual and team level and emphasizes the role of managers as shapers of the work environmental antecedents of WCB in the emergent digitalized working world. Theoretical implications and future research avenues are discussed

From dense to sparse design: Optimal rates under the supremum norm for estimating the mean function in functional data analysis

We derive optimal rates of convergence in the supremum norm for estimating the H\"older-smooth mean function of a stochastic process which is repeatedly and discretely observed with additional errors at fixed, multivariate, synchronous design points, the typical scenario for machine recorded functional data. Similarly to the optimal rates in $L_2$ obtained in \citet{cai2011optimal}, for sparse design a discretization term dominates, while in the dense case the parametric $\sqrt n$ rate can be achieved as if the $n$ processes were continuously observed without errors. The supremum norm is of practical interest since it corresponds to the visualization of the estimation error, and forms the basis for the construction uniform confidence bands. We show that in contrast to the analysis in $L_2$, there is an intermediate regime between the sparse and dense cases dominated by the contribution of the observation errors. Furthermore, under the supremum norm interpolation estimators which suffice in $L_2$ turn out to be sub-optimal in the dense setting, which helps to explain their poor empirical performance. In contrast to previous contributions involving the supremum norm, we discuss optimality even in the multivariate setting, and for dense design obtain the $\sqrt n$ rate of convergence without additional logarithmic factors. We also obtain a central limit theorem in the supremum norm, and provide simulations and real data applications to illustrate our results

Multi-level regulation of myotubularin-related protein-2 phosphatase activity by myotubularin-related protein-13/set-binding factor-2

Mutations in myotubularin-related protein-2 (MTMR2) or MTMR13/set-binding factor-2 (SBF2) genes are responsible for the severe autosomal recessive hereditary neuropathies, Charcot-Marie-Tooth disease (CMT) types 4B1 and 4B2, both characterized by reduced nerve conduction velocities, focally folded myelin sheaths and demyelination. MTMRs form a large family of conserved dual-specific phosphatases with enzymatically active and inactive members. We show that homodimeric active Mtmr2 interacts with homodimeric inactive Sbf2 in a tetrameric complex. This association dramatically increases the enzymatic activity of the complexed Mtmr2 towards phosphatidylinositol 3-phosphate and phosphatidylinositol 3,5-bisphosphate. Mtmr2 and Sbf2 are considerably, but not completely, co-localized in the cellular cytoplasm. On membranes of large vesicles formed under hypo-osmotic conditions, Sbf2 favorably competes with Mtmr2 for binding sites. Our data are consistent with a model suggesting that, at a given cellular location, Mtmr2 phosphatase activity is highly regulated, being high in the Mtmr2/Sbf2 complex, moderate if Mtmr2 is not associated with Sbf2 or functionally blocked by competition through Sbf2 for membrane-binding site