Consistent ultrafinitist logic

Ultrafinitism postulates that we can only compute on relatively short objects, and numbers beyond certain value are not available. This approach would also forbid many forms of infinitary reasoning and allow to remove certain paradoxes stemming from enumeration theorems. However, philosophers still disagree of whether such a finitist logic would be consistent. We present preliminary work on a proof system based on Curry-Howard isomorphism. We also try to present some well-known theorems that stop being true in such systems, whereas opposite statements become provable. This approach presents certain impossibility results as logical paradoxes stemming from a profligate use of transfinite reasoning.Comment: First submitted to CiE2021 in January, under review for GandALF2021. Contains inference rules, and polynomial reduction rule

Curious properties of latency distributions

Network latency distributions, their algebra, and use examples. This paper considers modeling of capacity-insensitive processes and distributed systems. It provides algebraic properties of the latency distribution algebra and Haskell code to implement the model

Two component Bose-Hubbard model with higher angular momentum states

We study a Bose-Hubbard Hamiltonian of ultracold two component gas of spinor Chromium atoms. Dipolar interactions of magnetic moments while tuned resonantly by ultralow magnetic field can lead to spin flipping. Due to approximate axial symmetry of individual lattice site, total angular momentum is conserved. Therefore, all changes of the spin are accompanied by the appearance of the angular orbital momentum. This way excited Wannier states with non vanishing angular orbital momentum can be created. Resonant dipolar coupling of the two component Bose gas introduces additional degree of control of the system, and leads to a variety of different stable phases. The phase diagram for small number of particles is discussed.Comment: 4 pages, 2 figure

TEMPERED RELAXATION EQUATION AND RELATED GENERALIZED STABLE PROCESSES

Fractional relaxation equations, as well as relaxation functions time-changed by independent stochastic processes have been widely studied (see, for example, MAI, STAW and GAR). We start here by proving that the upper-incomplete Gamma function satisfies the tempered-relaxation equation (of index ρ∈(0,1)); thanks to this explicit form of the solution, we can then derive its spectral distribution, which extends the stable law. Accordingly, we define a new class of selfsimilar processes (by means of the n-times Laplace transform of its density) which is indexed by the parameter ρ: in the special case where ρ=1, it reduces to the stable subordinator. Therefore the parameter ρ can be seen as a measure of the local deviation from the temporal dependence structure displayed in the standard stable case

Development of laser technology in Poland

The paper presents chosen development threads of laser technology and associated branches of optoelectronics in this country. An occasion to summarize the work and show their current status is the 50 th anniversary of construction of the first laser. The first laser in Poland was launched successfully in 1969, almost simultaneously at WAT and PW. Domestic achievements in this area are summarized every three years by Symposium on Laser Technology held traditionally in Swinoujscie. The work carried on in Poland concerns technology of laser materials, construction of new lasers and associated equipment as well as laser applications. Many technical teams participate in laser oriented European structural and framework projects. Ths is an invited paper to present participation of Polish teams in such European projects as EuCARD - European Coordination of Accelerator Research, FLASH - Free ELctron Laser in DESY Hamburg, E-XFEL - European X-Ray FEL, ELI - Extreme Light Infrastructure, and HIPER

On the stability of Bose-Fermi mixtures

We consider the stability of a mixture of degenerate Bose and Fermi gases. Even though the bosons effectively repel each other the mixture can still collapse provided the Bose and Fermi gases attract each other strongly enough. For a given number of atoms and the strengths of the interactions between them we find the geometry of a maximally compact trap that supports the stable mixture. We compare a simple analytical estimation for the critical axial frequency of the trap with results based on the numerical solution of hydrodynamic equations for Bose-Fermi mixture.Comment: 4 pages, 3 figure

Paternal Care in Collared Lemmings (Dicrostonyx richardsoni): Artifact or Adaptation?

Experiments conducted in large enclosures using 13 pairs of collared lemmings (Dicrostonyx richardsoni) and their pups examined the effects of three different treatments on paternal care. Treatments tested whether males altered their attentiveness to the pups when certainty of paternity was in question (through presence of a strange male), when alternative activities were available (through access to a running wheel), and when both factors were present simultaneously. Males covered and groomed pups equally among treatments. During the first five days of observation, males with access to a running wheel paid significantly less attention to strange males relative to males without access to a running wheel. Continuous exposure to the strange male may have been responsible for this short-term effect. Since covering and grooming of pups were unaffected by the presence of a strange male, the fathers' perceptions of their certainty of paternity were probably unaffected. Maintenance of paternal care under different conditions and in large enclosures provides further evidence that paternal care is not an artifact of laboratory conditions. Paternal care in collared lemmings may have evolved to maximize fitness of both sexes during winter.Key words: collared lemming, paternal care, winter breeding, fitnessDes expériences menées dans de grands enclos, et mettant en jeu 13 couples de lemmings à collerette (Dicrostonyx richardsonii) et leurs petits, évaluaient les effets de 3 traitements différents sur les soins paternels. Ces traitements vérifiaient si les mâles modifiaient l'attention qu'ils portaient à leurs petits lorsque leur paternité était mise en doute (par la présence d'un mâle étranger), lorsque d'autres activités étaient disponibles (par l'accès à une roue d'exercice), et lorsque ces 2 facteurs étaient présents en même temps. Les mâles protégeaient leurs petits et les nettoyaient de la même façon lors des différents traitements. Au cours des 5 premiers jours d'observation, les mâles qui avaient accès à une roue d'exercice prêtaient nettement moins attention aux mâles étrangers, comparativement aux mâles qui n'avaient pas accès à une roue. L'exposition continue au mâle étranger peut expliquer cet effet à court terme. Vu que les soins visant à protéger et à nettoyer les petits n'étaient pas affectés par la présence d'un mâle étranger, la perception qu'avaient les pères quant à la certitude de leur paternité n'était probablement pas affectée. Le maintien des soins paternels dans différentes conditions et à l'intérieur de grands enclos offre une preuve supplémentaire à l'appui que ces soins ne sont pas créés par les conditions de laboratoire. Les soins paternels chez le lemming à collerette ont peut-être évolué afin de maximiser la santé physique des 2 sexes en période hivernale.Mots clés : lemming à collerette, soins paternels, reproduction hivernale, santé physiqu