On Recurrent Reachability for Continuous Linear Dynamical Systems

The continuous evolution of a wide variety of systems, including continuous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether the solution $\boldsymbol{x}(t)$ of a system of linear differential equations $d\boldsymbol{x}/dt=A\boldsymbol{x}$ reaches a target halfspace infinitely often. This recurrent reachability problem can equivalently be formulated as the following Infinite Zeros Problem: does a real-valued function $f:\mathbb{R}_{\geq 0}\rightarrow\mathbb{R}$ satisfying a given linear differential equation have infinitely many zeros? Our main decidability result is that if the differential equation has order at most $7$, then the Infinite Zeros Problem is decidable. On the other hand, we show that a decision procedure for the Infinite Zeros Problem at order $9$ (and above) would entail a major breakthrough in Diophantine Approximation, specifically an algorithm for computing the Lagrange constants of arbitrary real algebraic numbers to arbitrary precision.Comment: Full version of paper at LICS'1

On the Turán number of some ordered even cycles

A classical result of Bondy and Simonovits in extremal graph theory states that if a graph on $n$ vertices contains no cycle of length $2k$ then it has at most $O(n^{1+1/k})$ edges. However, matching lower bounds are only known for $k=2,3,5$. In this paper we study ordered variants of this problem and prove some tight estimates for a certain class of ordered cycles that we call bordered cycles. In particular, we show that the maximum number of edges in an ordered graph avoiding bordered cycles of length at most $2k$ is $\Theta(n^{1+1/k})$. Strengthening the result of Bondy and Simonovits in the case of 6-cycles, we also show that it is enough to forbid these bordered orderings of the 6-cycle to guarantee an upper bound of $O(n^{4/3})$ on the number of edges.Comment: 10 pages, 1 figure; added references and some discussio

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete

Compensation between CSF1R+ macrophages and Foxp3+ Treg cells drives resistance to tumor immunotherapy

Redundancy and compensation provide robustness to biological systems but may contribute to therapy resistance. Both tumor-associated macrophages (TAMs) and Foxp3+ regulatory T (Treg) cells promote tumor progression by limiting antitumor immunity. Here we show that genetic ablation of CSF1 in colorectal cancer cells reduces the influx of immunosuppressive CSF1R+ TAMs within tumors. This reduction in CSF1-dependent TAMs resulted in increased CD8+ T cell attack on tumors, but its effect on tumor growth was limited by a compensatory increase in Foxp3+ Treg cells. Similarly, disruption of Treg cell activity through their experimental ablation produced moderate effects on tumor growth and was associated with elevated numbers of CSF1R+ TAMs. Importantly, codepletion of CSF1R+ TAMs and Foxp3+ Treg cells resulted in an increased influx of CD8+ T cells, augmentation of their function, and a synergistic reduction in tumor growth. Further, inhibition of Treg cell activity either through systemic pharmacological blockade of PI3Kdelta, or its genetic inactivation within Foxp3+ Treg cells, sensitized previously unresponsive solid tumors to CSF1R+ TAM depletion and enhanced the effect of CSF1R blockade. These findings identify CSF1R+ TAMs and PI3Kdelta-driven Foxp3+ Treg cells as the dominant compensatory cellular components of the immunosuppressive tumor microenvironment, with implications for the design of combinatorial immunotherapies

Hydrothermal dolomitization of basinal deposits controlled by a synsedimentary fault system in Triassic extensional setting, Hungary

Dolomitization of relatively thick carbonate successions occurs via an effective fluid circulation mechanism, since the replacement process requires a large amount of Mg-rich fluid interacting with the CaCO3 precursor. In the western end of the Neotethys, fault-controlled extensional basins developed during the Late Triassic spreading stage. In the Buda Hills and Danube-East blocks, distinct parts of silica and organic matter-rich slope and basinal deposits are dolomitized. Petrographic, geochemical, and fluid inclusion data distinguished two dolomite types: (1) finely to medium crystalline and (2) medium to coarsely crystalline. They commonly co-occur and show a gradual transition. Both exhibit breccia fabric under microscope. Dolomite texture reveals that the breccia fabric is not inherited from the precursor carbonates but was formed during the dolomitization process and under the influence of repeated seismic shocks. Dolomitization within the slope and basinal succession as well as within the breccia zones of the underlying basement block is interpreted as being related to fluid originated from the detachment zone and channelled along synsedimentary normal faults. The proposed conceptual model of dolomitization suggests that pervasive dolomitization occurred not only within and near the fault zones. Permeable beds have channelled the fluid towards the basin centre where the fluid was capable of partial dolomitization. The fluid inclusion data, compared with vitrinite reflectance and maturation data of organic matter, suggest that the ascending fluid was likely hydrothermal which cooled down via mixing with marine-derived pore fluid. Thermal gradient is considered as a potential driving force for fluid flow

Similarities and differences in the dolomitization history of two coeval Middle Triassic carbonate platforms, Balaton Highland, Hungary

Dolomitization of platform carbonates is commonly the result of multiphase processes. Documentation of the complex dolomitization history is difficult if completely dolomitized sections are studied. Two Middle Anisian sections representing two coeval carbonate platforms were investigated and compared in the present study. Both sections are made up of meter-scale peritidal–lagoonal cycles with significant pedogenic overprint. One of the sections contains non-dolomitized, partially dolomitized, and completely dolomitized intervals, whereas the other is completely dolomitized. Based on investigations of the partially dolomitized section, penecontemporaneous dolomite formation and/or very early post-depositional dolomitization were identified in various lithofacies types. In shallow subtidal facies, porphyrotopic dolomite was found preferentially in microbial micritic fabrics. Microbially induced dolomite precipitation and/or progressive replacement of carbonate sediments could be interpreted for stromatolites. Cryptocrystalline to very finely crystalline dolomite, probably of pedogenic origin, was encountered in paleosoil horizons. Fabric-destructive dolomite commonly found below these horizons was likely formed via reflux of evaporated seawater. As a result of the different paleogeographic settings of the two platforms, their shallow-burial conditions were significantly different. One of the studied sections was located at the basinward platform margin where pervasive fabric-retentive dolomitization took place in a shallow-burial setting, probably via thermal convection. In contrast, in the area of the other, smaller platform shallow-water carbonates were covered by basinal deposits, preventing fluid circulation and accordingly pervasive shallow-burial dolomitization. In the intermediate to deep burial zone, recrystallization of partially dolomitized limestone and occlusion of newly opened fractures and pores by coarsely crystalline dolomite took place