On the complexity of edge labelings for trees

AbstractGiven a tree T with n edges and a set W of n weights, we deal with labelings of the edges of T with weights from W, optimizing certain objective functions. For some of these functions the optimization problem is shown to be NP-complete (e.g., finding a labeling with minimal diameter), and for others we find polynomial-time algorithms (e.g., finding a labeling with minimal average distance)

To what extent is Gluon Confinement an empirical fact?

Experimental verifications of Confinement in hadron physics have established the absence of charges with a fraction of the electron's charge by studying the energy deposited in ionization tracks at high energies, and performing Millikan experiments with charged droplets at rest. These experiments test only the absence of particles with fractional charge in the asymptotic spectrum, and thus "Quark" Confinement. However what theory suggests is that Color is confined, that is, all asymptotic particles are color singlets. Since QCD is a non-Abelian theory, the gluon force carriers (indirectly revealed in hadron jets) are colored. We empirically examine what can be said about Gluon Confinement based on the lack of detection of appropriate events, aiming at an upper bound for high-energy free-gluon production.Comment: 14 pages, 12 figures, version accepted at Few Body Physic

The INSIDEOUT framework provides precise signatures of the balance of intrinsic and extrinsic dynamics in brain states

Finding precise signatures of different brain states is a central, unsolved question in neuroscience. We reformulated the problem to quantify the 'inside out' balance of intrinsic and extrinsic brain dynamics in brain states. The difference in brain state can be described as differences in the detailed causal interactions found in the underlying intrinsic brain dynamics. We used a thermodynamics framework to quantify the breaking of the detailed balance captured by the level of asymmetry in temporal processing, i.e. the arrow of time. Specifically, the temporal asymmetry was computed by the time-shifted correlation matrices for the forward and reversed time series, reflecting the level of non-reversibility/non-equilibrium. We found precise, distinguishing signatures in terms of the reversibility and hierarchy of large-scale dynamics in three radically different brain states (awake, deep sleep and anaesthesia) in electrocorticography data from non-human primates. Significantly lower levels of reversibility were found in deep sleep and anaesthesia compared to wakefulness. Non-wakeful states also showed a flatter hierarchy, reflecting the diversity of the reversibility across the brain. Overall, this provides signatures of the breaking of detailed balance in different brain states, perhaps reflecting levels of conscious awareness

Strength-dependent perturbation of whole-brain model working in different regimes reveals the role of fluctuations in brain dynamics

Despite decades of research, there is still a lack of understanding of the role and generating mechanisms of the ubiquitous fluctuations and oscillations found in recordings of brain dynamics. Here, we used whole-brain computational models capable of presenting different dynamical regimes to reproduce empirical data's turbulence level. We showed that the model's fluctuations regime fitted to turbulence more faithfully reproduces the empirical functional connectivity compared to oscillatory and noise regimes. By applying global and local strength-dependent perturbations and subsequently measuring the responsiveness of the model, we revealed each regime's computational capacity demonstrating that brain dynamics is shifted towards fluctuations to provide much-needed flexibility. Importantly, fluctuation regime stimulation in a brain region within a given resting state network modulates that network, aligned with previous empirical and computational studies. Furthermore, this framework generates specific, testable empirical predictions for human stimulation studies using strength-dependent rather than constant perturbation. Overall, the whole-brain models fitted to the level of empirical turbulence together with functional connectivity unveil that the fluctuation regime best captures empirical data, and the strength-dependent perturbative framework demonstrates how this regime provides maximal flexibility to the human brain

Data-driven discovery of canonical large-scale brain dynamics

Human behavior and cognitive function correlate with complex patterns of spatio-temporal brain dynamics, which can be simulated using computational models with different degrees of biophysical realism. We used a data-driven optimization algorithm to determine and classify the types of local dynamics that enable the reproduction of different observables derived from functional magnetic resonance recordings. The phase space analysis of the resulting equations revealed a predominance of stable spiral attractors, which optimized the similarity to the empirical data in terms of the synchronization, metastability, and functional connectivity dynamics. For stable limit cycles, departures from harmonic oscillations improved the fit in terms of functional connectivity dynamics. Eigenvalue analyses showed that proximity to a bifurcation improved the accuracy of the simulation for wakefulness, while deep sleep was associated with increased stability. Our results provide testable predictions that constrain the landscape of suitable biophysical models, while supporting noise-driven dynamics close to a bifurcation as a canonical mechanism underlying the complex fluctuations that characterize endogenous brain activity

A terrestrial search for dark contents of the vacuum, such as dark energy, using atom interferometry

We describe the theory and first experimental work on our concept for searching on earth for the presence of dark content of the vacuum (DCV) using atom interferometry. Specifically, we have in mind any DCV that has not yet been detected on a laboratory scale, but might manifest itself as dark energy on the cosmological scale. The experimental method uses two atom interferometers to cancel the effect of earth's gravity and diverse noise sources. It depends upon two assumptions: first, that the DCV possesses some space inhomogeneity in density, and second that it exerts a sufficiently strong non-gravitational force on matter. The motion of the apparatus through the DCV should then lead to an irregular variation in the detected matter-wave phase shift. We discuss the nature of this signal and note the problem of distinguishing it from instrumental noise. We also discuss the relation of our experiment to what might be learned by studying the noise in gravitational wave detectors such as LIGO.The paper concludes with a projection that a future search of this nature might be carried out using an atom interferometer in an orbiting satellite. The apparatus is now being constructed

Low Energy Pion-Hyperon Interaction

We study the low energy pion-hyperon interaction considering effective non-linear chiral invariant Lagrangians including pions, rho mesons, hyperons and corresponding resonances. Then we calculate the S- and P-wave phase-shifts, total cross sections, angular distributions and polarizations for the momentum in the center-of-mass frame up to k=400 MeV. With these results we discuss the CP violation in the csi-> pi-lambda and omega-> pi-csi weak decays.Comment: 10 pages, 10 figure

Whole‐brain dynamics differentiate among cisgender and transgender individuals

How the brain represents gender identity is largely unknown, but some neural differences have recently been discovered. We used an intrinsic ignition framework to investigate whether there are gender differences in the propagation of neural activity across the whole-brain and within resting-state networks. Studying 29 trans men and 17 trans women with gender incongruence, 22 cis women, and 19 cis men, we computed the capability of a given brain area in space to propagate activity to other areas (mean-ignition), and the variability across time for each brain area (node-metastability). We found that both measurements differentiated all groups across the whole brain. At the network level, we found that compared to the other groups, cis men showed higher mean-ignition of the dorsal attention network and node-metastability of the dorsal and ventral attention, executive control, and temporal parietal networks. We also found higher mean-ignition values in cis men than in cis women within the executive control network, but higher mean-ignition in cis women than cis men and trans men for the default mode. Node-metastability was higher in cis men than cis women in the somatomotor network, while both mean-ignition and node-metastability were higher for cis men than trans men in the limbic network. Finally, we computed correlations between these measurements and a body image satisfaction score. Trans men's dissatisfaction as well as cis men's and cis women's satisfaction toward their own body image were distinctively associated with specific networks in each group. Overall, the study of the whole-brain network dynamical complexity discriminates gender identity groups, functional dynamic approaches could help disentangle the complex nature of the gender dimension in the brain

Approximation algorithms for maximally balanced connected graph partition

Given a simple connected graph $G = (V, E)$, we seek to partition the vertex set $V$ into $k$ non-empty parts such that the subgraph induced by each part is connected, and the partition is maximally balanced in the way that the maximum cardinality of these $k$ parts is minimized. We refer this problem to as {\em min-max balanced connected graph partition} into $k$ parts and denote it as {\sc $k$-BGP}. The general vertex-weighted version of this problem on trees has been studied since about four decades ago, which admits a linear time exact algorithm; the vertex-weighted {\sc $2$-BGP} and {\sc $3$-BGP} admit a $5/4$-approximation and a $3/2$-approximation, respectively; but no approximability result exists for {\sc $k$-BGP} when $k \ge 4$, except a trivial $k$-approximation. In this paper, we present another $3/2$-approximation for our cardinality {\sc $3$-BGP} and then extend it to become a $k/2$-approximation for {\sc $k$-BGP}, for any constant $k \ge 3$. Furthermore, for {\sc $4$-BGP}, we propose an improved $24/13$-approximation. To these purposes, we have designed several local improvement operations, which could be useful for related graph partition problems.Comment: 23 pages, 7 figures, accepted for presentation at COCOA 2019 (Xiamen, China