{SETH}-Based Lower Bounds for Subset Sum and Bicriteria Path

Subset-Sum and k-SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. One of the most intriguing open problems in this area is to base the hardness of one of these problems on the other. Our main result is a tight reduction from k-SAT to Subset-Sum on dense instances, proving that Bellman's 1962 pseudo-polynomial $O^{*}(T)$-time algorithm for Subset-Sum on $n$ numbers and target $T$ cannot be improved to time $T^{1-\varepsilon}\cdot 2^{o(n)}$ for any $\varepsilon>0$, unless the Strong Exponential Time Hypothesis (SETH) fails. This is one of the strongest known connections between any two of the core problems of fine-grained complexity. As a corollary, we prove a "Direct-OR" theorem for Subset-Sum under SETH, offering a new tool for proving conditional lower bounds: It is now possible to assume that deciding whether one out of $N$ given instances of Subset-Sum is a YES instance requires time $(N T)^{1-o(1)}$. As an application of this corollary, we prove a tight SETH-based lower bound for the classical Bicriteria s,t-Path problem, which is extensively studied in Operations Research. We separate its complexity from that of Subset-Sum: On graphs with $m$ edges and edge lengths bounded by $L$, we show that the $O(Lm)$ pseudo-polynomial time algorithm by Joksch from 1966 cannot be improved to $\tilde{O}(L+m)$, in contrast to a recent improvement for Subset Sum (Bringmann, SODA 2017)

A nonpolynomial Schroedinger equation for resonantly absorbing gratings

We derive a nonlinear Schroedinger equation with a radical term, in the form of the square root of (1-|V|^2), as an asymptotic model of the optical medium built as a periodic set of thin layers of two-level atoms, resonantly interacting with the electromagnetic field and inducing the Bragg reflection. A family of bright solitons is found, which splits into stable and unstable parts, exactly obeying the Vakhitov-Kolokolov criterion. The soliton with the largest amplitude, which is |V| = 1, is found in an explicit analytical form. It is a "quasi-peakon", with a discontinuity of the third derivative at the center. Families of exact cnoidal waves, built as periodic chains of quasi-peakons, are found too. The ultimate solution belonging to the family of dark solitons, with the background level |V| = 1, is a dark compacton, also obtained in an explicit analytical form. Those bright solitons which are unstable destroy themselves (if perturbed) attaining the critical amplitude, |V| = 1. The dynamics of the wave field around this critical point is studied analytically, revealing a switch of the system into an unstable phase. Collisions between bright solitons are investigated too. The collisions between fast solitons are quasi-elastic, while slowly moving ones merge into breathers, which may persist or perish (in the latter case, also by attaining |V| = 1).Comment: Physical Review A, in pres

Organisms in a changing world

Since its foundation in 1999 by Lawrence Hightower, the Cell Stress Society International (CSSI) has actively promoted international collaboration in the field of stress research. Over the years, the Society has gone from strength to strength, with one of its main, and highly, visible outputs being the journal ‘Cell Stress & Chaperones’. Although initially, the full title of the journal was ‘Cell Stress & Chaperones: An Integrative Journal of Stress Biology and Medicine’ with an emphasis on the medical feld, original scientifc articles were always welcomed from a wide range of organisms and diferent aspects of stress molecular biology. However, in 2020, the sub-title was expanded to ‘An Integrative Journal of Stress Biology, Medicine and the Environment’, in acknowledgement of the increasing importance of understanding the cellular stress response in nonmodel environmental species in the context of the current climate crisis. Initial plans to celebrate the change in subtitle with a special environmental issue were somewhat stymied by the COVID-19 pandemic. However, fnally, 3 years later, we are proud to present this special issue ‘Organisms in a Changing Environment’, which highlights the wide variety of stress response research being carried out in environmental species. In particular, these studies demonstrate how important it is to understand not only the environmental cellular stress response but also their integration with higher levels of biological organisation to understand future biodiversity, and inform conservation measures and policy in our changing world

Hyperfine Spectroscopy of Optically Trapped Atoms

We perform spectroscopy on the hyperfine splitting of $^{85}$Rb atoms trapped in far-off-resonance optical traps. The existence of a spatially dependent shift in the energy levels is shown to induce an inherent dephasing effect, which causes a broadening of the spectroscopic line and hence an inhomogeneous loss of atomic coherence at a much faster rate than the homogeneous one caused by spontaneous photon scattering. We present here a number of approaches for reducing this inhomogeneous broadening, based on trap geometry, additional laser fields, and novel microwave pulse sequences. We then show how hyperfine spectroscopy can be used to study quantum dynamics of optically trapped atoms.Comment: Review/Tutoria

Decomposition algorithms for submodular optimization with applications to parallel machine scheduling with controllable processing times

In this paper we present a decomposition algorithm for maximizing a linear function over a submodular polyhedron intersected with a box. Apart from this contribution to submodular optimization, our results extend the toolkit available in deterministic machine scheduling with controllable processing times. We demonstrate how this method can be applied to developing fast algorithms for minimizing total compression cost for preemptive schedules on parallel machines with respect to given release dates and a common deadline. Obtained scheduling algorithms are faster and easier to justify than those previously known in the scheduling literature

Separating Agent-Functioning and Inter-Agent Coordination by Activated Modules: The DECOMAS Architecture

The embedding of self-organizing inter-agent processes in distributed software applications enables the decentralized coordination system elements, solely based on concerted, localized interactions. The separation and encapsulation of the activities that are conceptually related to the coordination, is a crucial concern for systematic development practices in order to prepare the reuse and systematic integration of coordination processes in software systems. Here, we discuss a programming model that is based on the externalization of processes prescriptions and their embedding in Multi-Agent Systems (MAS). One fundamental design concern for a corresponding execution middleware is the minimal-invasive augmentation of the activities that affect coordination. This design challenge is approached by the activation of agent modules. Modules are converted to software elements that reason about and modify their host agent. We discuss and formalize this extension within the context of a generic coordination architecture and exemplify the proposed programming model with the decentralized management of (web) service infrastructures

Models and algorithms for energy-efficient scheduling with immediate start of jobs

We study a scheduling model with speed scaling for machines and the immediate start requirement for jobs. Speed scaling improves the system performance, but incurs the energy cost. The immediate start condition implies that each job should be started exactly at its release time. Such a condition is typical for modern Cloud computing systems with abundant resources. We consider two cost functions, one that represents the quality of service and the other that corresponds to the cost of running. We demonstrate that the basic scheduling model to minimize the aggregated cost function with n jobs is solvable in O(nlogn) time in the single-machine case and in O(n²m) time in the case of m parallel machines. We also address additional features, e.g., the cost of job rejection or the cost of initiating a machine. In the case of a single machine, we present algorithms for minimizing one of the cost functions subject to an upper bound on the value of the other, as well as for finding a Pareto-optimal solution

Crosstalk between glial and glioblastoma cells triggers the "go-or-grow" phenotype of tumor cells

Background: Glioblastoma (GBM), the most malignant primary brain tumor, leads to poor and unpredictable clinical outcomes. Recent studies showed the tumor microenvironment has a critical role in regulating tumor growth by establishing a complex network of interactions with tumor cells. In this context, we investigated how GBM cells modulate resident glial cells, particularly their paracrine activity, and how this modulation can influence back on the malignant phenotype of GBM cells. Methods: Conditioned media (CM) of primary mouse glial cultures unexposed (unprimed) or exposed (primed) to the secretome of GL261 GBM cells were analyzed by proteomic analysis. Additionally, these CM were used in GBM cells to evaluate their impact in glioma cell viability, migration capacity and activation of tumor-related intracellular pathways. Results: The proteomic analysis revealed that the pre-exposure of glial cells to CM from GBM cells led to the upregulation of several proteins related to inflammatory response, cell adhesion and extracellular structure organization within the secretome of primed glial cells. At the functional levels, CM derived from unprimed glial cells favored an increase in GBM cell migration capacity, while CM from primed glial cells promoted cells viability. These effects on GBM cells were accompanied by activation of particular intracellular cancer-related pathways, mainly the MAPK/ERK pathway, which is a known regulator of cell proliferation. Conclusions: Together, our results suggest that glial cells can impact on the pathophysiology of GBM tumors, and that the secretome of GBM cells is able to modulate the secretome of neighboring glial cells, in a way that regulates the "go-or-grow" phenotypic switch of GBM cells.Fundação para a Ciência e Tecnologia (IF/00601/2012 to B.M.C.; IF/00111 to A.J.S; SFRH/BD/52287/2013 to A.I.O.; SFRH/BD/81495/2011 to S.I.A.; SFRH/BD/88121/2012 to J.V.C.; projects PTDC/SAU-GMG/113795/2009 to B.M.C.; PTDC/NEU-NMC/0205/2012, PTDC/NEU-SCC/7051/2014, PEst-C/SAU/LA0001/2013–2014 and UID/NEU/04539/2013 to B.M.), Liga Portuguesa Contra o Cancro (B.M.C.), Fundação Calouste Gulbenkian (B.M.C.) and Inter-University Doctoral Programme in Ageing and Chronic Disease (PhDOC; to A.I.O.). Project co-financed by Programa Operacional Regional do Norte (ON.2—O Novo Norte), Quadro de Referência Estratégico Nacional (QREN), Fundo Europeu de Desenvolvimento Regional (FEDER), Programa Operacional Factores de Competitividade (COMPETE), and by The National Mass Spectrometry Network (RNEM) under the contract REDE/1506/REM/2005info:eu-repo/semantics/publishedVersio

The role of Allee effect in modelling post resection recurrence of glioblastoma

Resection of the bulk of a tumour often cannot eliminate all cancer cells, due to their infiltration into the surrounding healthy tissue. This may lead to recurrence of the tumour at a later time. We use a reaction-diffusion equation based model of tumour growth to investigate how the invasion front is delayed by resection, and how this depends on the density and behaviour of the remaining cancer cells. We show that the delay time is highly sensitive to qualitative details of the proliferation dynamics of the cancer cell population. The typically assumed logistic type proliferation leads to unrealistic results, predicting immediate recurrence. We find that in glioblastoma cell cultures the cell proliferation rate is an increasing function of the density at small cell densities. Our analysis suggests that cooperative behaviour of cancer cells, analogous to the Allee effect in ecology, can play a critical role in determining the time until tumour recurrence