TreeDQN: Learning to minimize Branch-and-Bound tree

Combinatorial optimization problems require an exhaustive search to find the optimal solution. A convenient approach to solving combinatorial optimization tasks in the form of Mixed Integer Linear Programs is Branch-and-Bound. Branch-and-Bound solver splits a task into two parts dividing the domain of an integer variable, then it solves them recursively, producing a tree of nested sub-tasks. The efficiency of the solver depends on the branchning heuristic used to select a variable for splitting. In the present work, we propose a reinforcement learning method that can efficiently learn the branching heuristic. We view the variable selection task as a tree Markov Decision Process, prove that the Bellman operator adapted for the tree Markov Decision Process is contracting in mean, and propose a modified learning objective for the reinforcement learning agent. Our agent requires less training data and produces smaller trees compared to previous reinforcement learning methods.Comment: Submitted to NeurIPS 202

Effect of Ultrahigh Stiffness of Defective Graphene from Atomistic Point of View

Well-known effect of mechanical stiffness degradation under the influence of point defects in macroscopic solids can be controversially reversed in the case of low-dimensional materials. Using atomistic simulation, we showed here that a single-layered graphene film can be sufficiently stiffened by monovacancy defects at a tiny concentration. Our results correspond well with recent experimental data and suggest that the effect of mechanical stiffness augmentation is mainly originated from specific bonds distribution in the surrounded monovacancy defects regions. We showed that such unusual mechanical response is the feature of presence of specifically monovacancies, whereas other types of point defects such as divacancy, 555-777 and Stone-Wales defects, lead to the ordinary degradation of the graphene mechanical stiffness.Comment: 9 pages, 3 figure

Spontaneously Broken 3d Hietarinta/Maxwell Chern-Simons Theory and Minimal Massive Gravity

We show that minimal massive 3d gravity (MMG), as well as the topological massive gravity, are particular cases of a more general `minimal massive gravity' theory (with a single massive propagating mode) arising upon spontaneous breaking of a local symmetry in a Chern-Simons gravity based on a Hietarinta or Maxwell algebra. Similar to the MMG case, the requirements that the propagating massive mode is neither tachyon nor ghost and that the central charges of an asymptotic algebra associated with a boundary CFT are positive, impose restrictions on the range of the parameters of the theory.Comment: 30 pages, v.2: typos corrected comments and references adde

In Search of Needles in a 11M Haystack: Recurrent Memory Finds What LLMs Miss

This paper addresses the challenge of processing long documents using generative transformer models. To evaluate different approaches, we introduce BABILong, a new benchmark designed to assess model capabilities in extracting and processing distributed facts within extensive texts. Our evaluation, which includes benchmarks for GPT-4 and RAG, reveals that common methods are effective only for sequences up to $10^4$ elements. In contrast, fine-tuning GPT-2 with recurrent memory augmentations enables it to handle tasks involving up to $11\times 10^6$ elements. This achievement marks a substantial leap, as it is by far the longest input processed by any neural network model to date, demonstrating a significant improvement in the processing capabilities for long sequences.Comment: 11M tokens, fix qa3 min facts per task in Table

Displacement current during the formation of positive streamers in atmospheric pressure air with a highly inhomogeneous electric field

This paper presents experimental data on the dynamics of positive streamers formation in a highly inhomogeneous electric field under threshold for the breakdown of the gap conditions as well as at high voltage. The glow of the streamer was registered with a four-channel intensified charge-coupled device camera with simultaneous recording of voltage and current characteristics per pulse. It was shown that the streamer appearance is accompanied by a displacement current pulse induced by a redistribution of the electric field strength in the gap. We call this current the dynamic displacement current (DDC). The DDC value changes during the streamer propagation in the gap. It reaches the maximum values when the streamer starts and when it is close to bridge the gap. The DDC was also registered with a collector placed behind the grid plane electrode which is usually applied for the registration of runaway electrons when a negative streamer is formed. It was shown that the DDC allows to study the features of the streamer formation

Blue and green jets in laboratory discharges initiated by runaway electrons

Spectral and amplitude-temporal characteristics of plasma radiation of nanosecond pulse-periodic discharge in air, nitrogen and argon in pressure range of 30-760 Torr were investigated. Discharge gap geometry was a "point-to-plane". Voltage pulses of negative polarity (amplitude, FWHM and risetime was 13 kV, 10 ns and 4 ns, respectively) were applied to a pointed cathode made of different metals (stainless steel, aluminum and copper). Jets of different colour were observed near a cathode tip. They are formed due to explosive emission. Colour of jets depends on the cathode material. Intense lines of the atoms and ions of iron in the wavelength range of 200-600 nm, aluminum with λ = 394.4, 396.15 nm, including multiply charged ion Al VI with λ = 360.39 and 361.65 nm, copper with λ = 324.8, 327.3, 510.6, 515.3, 521.8, 522 nm were registered. The resonance energy transfer from metastable A3Π+u level of nitrogen molecule to 3d104p level of Cu I was found. As a result a luminescence duration of Cu I was about 1.5 μs at duration of discharge current of 1.5 ps. During constriction of the diffuse discharge the sputtering of material occurs in the direction perpendicular to the longitudinal axis of the discharge gap

Economic Theory, Economic Reality and Economic Policy

This paper analyzes the opposition between the «liberals» and «statists» in the Russian political and economic thought. It demonstrates that the economic liberalization is an absolute prerequisite for the transition to sustainable socio-economic development. Such development must rely on investment activities of the state, which in the current circumstances is a necessary but not sufficient measure for reversing the negative trends. The negative developments can be prevented only through implementation, along with the institutional changes in the economic area that form a strata of economically independent entrepreneursinnovators, of no less profound transformation in political institutions aimed at democratization of public life