Tight Complexity Bounds for Counting Generalized Dominating Sets in Bounded-Treewidth Graphs

We investigate how efficiently a well-studied family of domination-type problems can be solved on bounded-treewidth graphs. For sets $\sigma,\rho$ of non-negative integers, a $(\sigma,\rho)$-set of a graph $G$ is a set $S$ of vertices such that $|N(u)\cap S|\in \sigma$ for every $u\in S$, and $|N(v)\cap S|\in \rho$ for every $v\not\in S$. The problem of finding a $(\sigma,\rho)$-set (of a certain size) unifies standard problems such as Independent Set, Dominating Set, Independent Dominating Set, and many others. For all pairs of finite or cofinite sets $(\sigma,\rho)$, we determine (under standard complexity assumptions) the best possible value $c_{\sigma,\rho}$ such that there is an algorithm that counts $(\sigma,\rho)$-sets in time $c_{\sigma,\rho}^{\sf tw}\cdot n^{O(1)}$ (if a tree decomposition of width ${\sf tw}$ is given in the input). For example, for the Exact Independent Dominating Set problem (also known as Perfect Code) corresponding to $\sigma=\{0\}$ and $\rho=\{1\}$, we improve the $3^{\sf tw}\cdot n^{O(1)}$ algorithm of [van Rooij, 2020] to $2^{\sf tw}\cdot n^{O(1)}$. Despite the unusually delicate definition of $c_{\sigma,\rho}$, we show that our algorithms are most likely optimal, i.e., for any pair $(\sigma, \rho)$ of finite or cofinite sets where the problem is non-trivial, and any $\varepsilon>0$, a $(c_{\sigma,\rho}-\varepsilon)^{\sf tw}\cdot n^{O(1)}$-algorithm counting the number of $(\sigma,\rho)$-sets would violate the Counting Strong Exponential-Time Hypothesis (#SETH). For finite sets $\sigma$ and $\rho$, our lower bounds also extend to the decision version, showing that our algorithms are optimal in this setting as well. In contrast, for many cofinite sets, we show that further significant improvements for the decision and optimization versions are possible using the technique of representative sets

Tight Complexity Bounds for Counting Generalized Dominating Sets in Bounded-Treewidth Graphs

We investigate how efficiently a well-studied family of domination-type problems can be solved on bounded-treewidth graphs. For sets $\sigma,\rho$ of non-negative integers, a $(\sigma,\rho)$-set of a graph $G$ is a set $S$ of vertices such that $|N(u)\cap S|\in \sigma$ for every $u\in S$, and $|N(v)\cap S|\in \rho$ for every $v\not\in S$. The problem of finding a $(\sigma,\rho)$-set (of a certain size) unifies standard problems such as \textsc{Independent Set}, \textsc{Dominating Set}, \textsc{Independent Dominating Set}, and many others. For almost all pairs of finite or cofinite sets $(\sigma,\rho)$, we determine (under standard complexity assumptions) the best possible value $c_{\sigma,\rho}$ such that there is an algorithm that counts $(\sigma,\rho)$-sets in time c_{\sigma,\rho}^\tw\cdot n^{\O(1)} (if a tree decomposition of width \tw is given in the input). Let \sigMax denote the largest element of $\sigma$ if $\sigma$ is finite, or the largest missing integer $+1$ if $\sigma$ is cofinite; \rhoMax is defined analogously for $\rho$. Surprisingly, $c_{\sigma,\rho}$ is often significantly smaller than the natural bound \sigMax+\rhoMax+2 achieved by existing algorithms [van Rooij, 2020]. Toward defining $c_{\sigma,\rho}$, we say that $(\sigma, \rho)$ is \mname-structured if there is a pair $(\alpha,\beta)$ such that every integer in $\sigma$ equals $\alpha$ mod \mname, and every integer in $\rho$ equals $\beta$ mod \mname. Then, setting \begin{itemize} \item c_{\sigma,\rho}=\max\{\sigMax,\rhoMax\}+1 if $(\sigma,\rho)$ is \mname-structured for some \mname \ge 3, or 2-structured with \sigMax\neq \rhoMax, or 2-structured with \sigMax=\rhoMax being odd, \item c_{\sigma,\rho}=\max\{\sigMax,\rhoMax\}+2 if $(\sigma,\rho)$ is 2-structured, but not \mname-structured for any \mname \ge 3, and \sigMax=\rhoMax is even, and \item c_{\sigma,\rho}=\sigMax+\rhoMax+2 if $(\sigma,\rho)$ is not \mname-structured for any \mname\ge 2, \end{itemize} we provide algorithms counting $(\sigma,\rho)$-sets in time c_{\sigma,\rho}^\tw\cdot n^{\O(1)}. For example, for the \textsc{Exact Independent Dominating Set} problem (also known as \textsc{Perfect Code}) corresponding to $\sigma=\{0\}$ and $\rho=\{1\}$, this improves the 3^\tw\cdot n^{\O(1)} algorithm of van Rooij to 2^\tw\cdot n^{\O(1)}. Despite the unusually delicate definition of $c_{\sigma,\rho}$, we show that our algorithms are most likely optimal, i.e., for any pair $(\sigma, \rho)$ of finite or cofinite sets where the problem is non-trivial (except those having cofinite $\sigma$ with $\rho=\mathbb Z_{\ge0}$), and any $\varepsilon>0$, a (c_{\sigma,\rho}-\varepsilon)^\tw\cdot n^{\O(1)}-algorithm counting the number of $(\sigma,\rho)$-sets would violate the Counting Strong Exponential-Time Hypothesis (\#SETH). For finite sets $\sigma$ and $\rho$, our lower bounds also extend to the decision version, showing that our algorithms are optimal in this setting as well. In contrast, for many cofinite sets, we show that further significant improvements for the decision and optimization versions are possible using the technique of representative sets

Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice

Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications from high temperature superconductors to spintronic devices. Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers due to the extreme complexity arising from quantum entanglement between the constituent magnetic spins. Here we employ a degenerate Bose gas confined in an optical lattice to simulate a chain of interacting quantum Ising spins as they undergo a phase transition. Strong spin interactions are achieved through a site-occupation to pseudo-spin mapping. As we vary an applied field, quantum fluctuations drive a phase transition from a paramagnetic phase into an antiferromagnetic phase. In the paramagnetic phase the interaction between the spins is overwhelmed by the applied field which aligns the spins. In the antiferromagnetic phase the interaction dominates and produces staggered magnetic ordering. Magnetic domain formation is observed through both in-situ site-resolved imaging and noise correlation measurements. By demonstrating a route to quantum magnetism in an optical lattice, this work should facilitate further investigations of magnetic models using ultracold atoms, improving our understanding of real magnetic materials.Comment: 12 pages, 9 figure

Absence of system xc⁻ on immune cells invading the central nervous system alleviates experimental autoimmune encephalitis

Background: Multiple sclerosis (MS) is an autoimmune demyelinating disease that affects the central nervous system (CNS), leading to neurodegeneration and chronic disability. Accumulating evidence points to a key role for neuroinflammation, oxidative stress, and excitotoxicity in this degenerative process. System x(c)- or the cystine/glutamate antiporter could tie these pathological mechanisms together: its activity is enhanced by reactive oxygen species and inflammatory stimuli, and its enhancement might lead to the release of toxic amounts of glutamate, thereby triggering excitotoxicity and neurodegeneration. Methods: Semi-quantitative Western blotting served to study protein expression of xCT, the specific subunit of system x(c)-, as well as of regulators of xCT transcription, in the normal appearing white matter (NAWM) of MS patients and in the CNS and spleen of mice exposed to experimental autoimmune encephalomyelitis (EAE), an accepted mouse model of MS. We next compared the clinical course of the EAE disease, the extent of demyelination, the infiltration of immune cells and microglial activation in xCT-knockout (xCT(-/-)) mice and irradiated mice reconstituted in xCT(-/-) bone marrow (BM), to their proper wild type (xCT(+/+)) controls. Results: xCT protein expression levels were upregulated in the NAWM of MS patients and in the brain, spinal cord, and spleen of EAE mice. The pathways involved in this upregulation in NAWM of MS patients remain unresolved. Compared to xCT(+/+) mice, xCT(-/-) mice were equally susceptible to EAE, whereas mice transplanted with xCT(-/-) BM, and as such only exhibiting loss of xCT in their immune cells, were less susceptible to EAE. In none of the above-described conditions, demyelination, microglial activation, or infiltration of immune cells were affected. Conclusions: Our findings demonstrate enhancement of xCT protein expression in MS pathology and suggest that system x(c)- on immune cells invading the CNS participates to EAE. Since a total loss of system x(c)- had no net beneficial effects, these results have important implications for targeting system x(c)- for treatment of MS

Quantum Criticality in Heavy Fermion Metals

Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. Heavy fermion metals have in recent years emerged as prototypical systems to study quantum critical points. There have been considerable efforts, both experimental and theoretical, which use these magnetic systems to address problems that are central to the broad understanding of strongly correlated quantum matter. Here, we summarize some of the basic issues, including i) the extent to which the quantum criticality in heavy fermion metals goes beyond the standard theory of order-parameter fluctuations, ii) the nature of the Kondo effect in the quantum critical regime, iii) the non-Fermi liquid phenomena that accompany quantum criticality, and iv) the interplay between quantum criticality and unconventional superconductivity.Comment: (v2) 39 pages, 8 figures; shortened per the editorial mandate; to appear in Nature Physics. (v1) 43 pages, 8 figures; Non-technical review article, intended for general readers; the discussion part contains more specialized topic

Repetition benefit in mental rotation is independent of stimulus repetition

In this study, we investigated whether there is a repetition benefit in mental rotation that is independent of stimulus repetition (i.e., due to increased efficiency in postencoding processing). Three experiments were conducted, in which different conditions of stimulus repetition (different letters on consecutive trials in Experiment 1, letters of different orientations on consecutive trials in Experiment 2, and priming of rotation direction in Experiment 3) were used, and the extent of repetition of rotation direction between two consecutive trials was manipulated. The results of all three experiments showed clear evidence of a repetition benefit without repeating the stimulus, suggesting that this effect is independent of stimulus repetition and lending support to the notion of increased efficiency in mental rotation as a result of repeated rotation direction per se

Fluorescence Lifetime Imaging Unravels C. trachomatis Metabolism and Its Crosstalk with the Host Cell

Chlamydia trachomatis is an obligate intracellular bacterium that alternates between two metabolically different developmental forms. We performed fluorescence lifetime imaging (FLIM) of the metabolic coenzymes, reduced nicotinamide adenine dinucleotides [NAD(P)H], by two-photon microscopy for separate analysis of host and pathogen metabolism during intracellular chlamydial infections. NAD(P)H autofluorescence was detected inside the chlamydial inclusion and showed enhanced signal intensity on the inclusion membrane as demonstrated by the co-localization with the 14-3-3β host cell protein. An increase of the fluorescence lifetime of protein-bound NAD(P)H [τ2-NAD(P)H] inside the chlamydial inclusion strongly correlated with enhanced metabolic activity of chlamydial reticulate bodies during the mid-phase of infection. Inhibition of host cell metabolism that resulted in aberrant intracellular chlamydial inclusion morphology completely abrogated the τ2-NAD(P)H increase inside the chlamydial inclusion. τ2-NAD(P)H also decreased inside chlamydial inclusions when the cells were treated with IFNγ reflecting the reduced metabolism of persistent chlamydiae. Furthermore, a significant increase in τ2-NAD(P)H and a decrease in the relative amount of free NAD(P)H inside the host cell nucleus indicated cellular starvation during intracellular chlamydial infection. Using FLIM analysis by two-photon microscopy we could visualize for the first time metabolic pathogen-host interactions during intracellular Chlamydia trachomatis infections with high spatial and temporal resolution in living cells. Our findings suggest that intracellular chlamydial metabolism is directly linked to cellular NAD(P)H signaling pathways that are involved in host cell survival and longevity

Biventricular myocardial strain analysis in patients with arrhythmogenic right ventricular cardiomyopathy (ARVC) using cardiovascular magnetic resonance feature tracking

BACKGROUND: Fibrofatty degeneration of myocardium in ARVC is associated with wall motion abnormalities. The aim of this study was to examine whether Cardiovascular Magnetic Resonance (CMR) based strain analysis using feature tracking (FT) can serve as a quantifiable measure to confirm global and regional ventricular dysfunction in ARVC patients and support the early detection of ARVC. METHODS: We enrolled 20 patients with ARVC, 30 with borderline ARVC and 22 subjects with a positive family history but no clinical signs of a manifest ARVC. 10 healthy volunteers (HV) served as controls. 15 ARVC patients received genotyping for Plakophilin-2 mutation (PKP-2), of which 7 were found to be positive. Cine MR datasets of all subjects were assessed for myocardial strain using FT (TomTec Diogenes Software). Global strain and strain rate in radial, circumferential and longitudinal mode were assessed for the right and left ventricle. In addition strain analysis at a segmental level was performed for the right ventricular free wall. RESULTS: RV global longitudinal strain rates in ARVC (−0.68 ± 0.36 sec(−1)) and borderline ARVC (−0.85 ± 0.36 sec(−1)) were significantly reduced in comparison with HV (−1.38 ± 0.52 sec(−1), p ≤ 0.05). Furthermore, in ARVC patients RV global circumferential strain and strain rates at the basal level were significantly reduced compared with HV (strain: −5.1 ± 2.7 vs. -9.2 ± 3.6%; strain rate: −0.31 ± 0.13 sec(−1) vs. -0.61 ± 0.21 sec(−1)). Even for patients with ARVC or borderline ARVC and normal RV ejection fraction (n=30) global longitudinal strain rate proved to be significantly reduced compared with HV (−0.9 ± 0.3 vs. -1.4 ± 0.5 sec(−1); p < 0.005). In ARVC patients with PKP-2 mutation there was a clear trend towards a more pronounced impairment in RV global longitudinal strain rate. On ROC analysis RV global longitudinal strain rate and circumferential strain rate at the basal level proved to be the best discriminators between ARVC patients and HV (AUC: 0.9 and 0.92, respectively). CONCLUSION: CMR based strain analysis using FT is an objective and useful measure for quantification of wall motion abnormalities in ARVC. It allows differentiation between manifest or borderline ARVC and HV, even if ejection fraction is still normal

Expression of Transketolase like gene 1 (TKTL1) predicts disease-free survival in patients with locally advanced rectal cancer receiving neoadjuvant chemoradiotherapy

<p>Abstract</p> <p>Background</p> <p>For patients with locally advanced rectal cancer (LARC) neoadjuvant chemoradiotherapy is recommended as standard therapy. So far, no predictive or prognostic molecular factors for patients undergoing multimodal treatment are established. Increased angiogenesis and altered tumour metabolism as adaption to hypoxic conditions in cancers play an important role in tumour progression and metastasis. Enhanced expression of Vascular-endothelial-growth-factor-receptor <it>(VEGF-R</it>) and Transketolase-like-1 (<it>TKTL1</it>) are related to hypoxic conditions in tumours. In search for potential prognostic molecular markers we investigated the expression of <it>VEGFR-1</it>, <it>VEGFR-2 </it>and <it>TKTL1 </it>in patients with LARC treated with neoadjuvant chemoradiotherapy and cetuximab.</p> <p>Methods</p> <p>Tumour and corresponding normal tissue from pre-therapeutic biopsies of 33 patients (m: 23, f: 10; median age: 61 years) with LARC treated in phase-I and II trials with neoadjuvant chemoradiotherapy (cetuximab, irinotecan, capecitabine in combination with radiotherapy) were analysed by quantitative PCR.</p> <p>Results</p> <p>Significantly higher expression of <it>VEGFR-1/2 </it>was found in tumour tissue in pre-treatment biopsies as well as in resected specimen after neoadjuvant chemoradiotherapy compared to corresponding normal tissue. High <it>TKTL1 </it>expression significantly correlated with disease free survival. None of the markers had influence on early response parameters such as tumour regression grading. There was no correlation of gene expression between the investigated markers.</p> <p>Conclusion</p> <p>High <it>TKTL-1 </it>expression correlates with poor prognosis in terms of 3 year disease-free survival in patients with LARC treated with intensified neoadjuvant chemoradiotherapy and may therefore serve as a molecular prognostic marker which should be further evaluated in randomised clinical trials.</p

The 1958–2009 Greenland ice sheet surface melt and the mid-tropospheric atmospheric circulation

peer reviewedaudience: researcherIn order to assess the impact of the mid-tropospheric circulation over the Greenland ice sheet (GrIS) on surface melt, as simulated by the regional climate model MAR, an automatic Circulation type classification (CTC) based on 500 hPa geopotential height from reanalyses is developed. General circulation correlates significantly with the surface melt anomalies for the summers in the period 1958–2009. The record surface melt events observed during the summers of 2007–2009 are linked to the exceptional persistence of atmospheric circulations favouring warm air advection. The CTC emphasizes that summer 500 hPa circulation patterns have changed since the beginning of the 2000s; this process is partly responsible for the recent warming observed over the GrIS