Black hole entropy calculation from near horizon symmetries

U ovom radu pokazali smo jedan način za računanje entropije (2+1) stacionarne crne rupe. Pri tome smo koristili dimenzionalnu redukciju na dvije dimenzije što je rezultiralo dilatonskim modelom te simetrije na horizontu crne rupe. Za generatore tih simetrija je pokazano da zadovoljavaju Virasoro algebru što nam je omogućilo korištenje Cardyjeve formule za entropiju. Rezultat koji smo dobili slaže se s Bekenstein-Hawkingovom formulom za entropiju.In this paper we showed one way to compute the entropy of (2+1) stationary black hole. We did so by using dimensional reduction on two dimensions, which resulted in dilaton model, and symmetries on the black hole horizon. It has been shown that generators of those symmetries satisfy Virasoro algebra which allowed us to use Cardy formula for entropy. The result is consistent with Bekenstein-Hawking formula

Dirac sigma models from gauging the nonlinear sigma models and its BV action

We present the construction of the Dirac sigma models by gauging the 2-dimensional nonlinear sigma models, but also including the possibility of nonminimal coupling to the metric sector. We show that for a large variety of possible cases, the minimal coupling to the metric sector is the only nontrivial possibility. In addition, we present the construction of the classical Batalin-Vilkovisky action for the Dirac sigma models. We follow a direct approach in its construction, by requiring it to be a solution of the classical master equation.Comment: Written for Proceeding in Science, 18 page

Konvergencija cikličke Jacobijeve metode za hermitsku matricu reda 4

U ovom radu prikazali smo Jacobijevu metodu za hermitske matrice reda 4 definiranu općom cikličkom pivotnom strategijom. Uveli smo relacije ekvivalencije \sim, \underaccent{\tilde}{s}, \underaccent{\tilde}{w}, \underaccent{\tilde}{p} na skupu svih cikličkih strategija te pokazali da konvergenost metode pod nekom strategijom povlači konvergentnost metode pod njoj ekvivalentnom strategijom. Zatim smo pokazali globalnu konvergenciju metode pod strategijama iz specijalne familije $C_1$ te pod jednom paralelnom strategijom. Pomoću računalnog programa podijelili smo 720 cikličkih strategija u 5 klasa ekvivalencije, te u svakoj klasi pronašli strategiju za koju smo pokazali globalnu konvergenciju. To je bilo dovoljno da se pokaže globalna konvergencija metode pod svih 720 cikličkih strategija.In this work we have presented the Jacobi method for Hermitian matrices of order 4 defined by a general cyclic pivot strategy. We have introduced equivalence relations \sim, \underaccent{\tilde}{s}, \underaccent{\tilde}{w}, \underaccent{\tilde}{p} on the set of cyclic strategies and shown that convergence of the method under some strategy implies convergence of the method under an equivalent strategy. Then we have shown the global convergence of the method under the strategies from the special family $C_1$ and under one parallel strategy. Using a computer program, we have partitioned the set of 720 cyclic strategies in 5 equivalence classes. For each class we have found a strategy for which the method is convergent. That is enough to show the global convergence of the method under all 720 cyclic strategies

Exactly solvable spin- 1/2 XYZ models with highly degenerate partially ordered ground states

Exactly solvable models play a special role in condensed matter physics, serving as secure theoretical starting points for investigation of new phenomena. Changlani et al. [Phys. Rev. Lett. 120, 117202 (2018)] have discovered a limit of the XXZ model for S=1/2 spins on the kagome lattice, which is not only exactly solvable, but features a huge degeneracy of exact ground states corresponding to solutions of a three-coloring problem. This special point of the model was proposed as a parent for multiple phases in the wider phase diagram, including quantum spin liquids. Here, we show that the construction of Changlani et al. can be extended to more general forms of anisotropic exchange interaction, finding a line of parameter space in an XYZ model which maintains both the macroscopic degeneracy and the three-coloring structure of solutions. We show that the ground states along this line are partially ordered, in the sense that infinite-range correlations of some spin components coexist with a macroscopic number of undetermined degrees of freedom. We therefore propose the exactly solvable limit of the XYZ model on corner-sharing triangle-based lattices as a tractable starting point for discovery of quantum spin systems which mix ordered and spin-liquid-like properties

Crushing energy measurements on the field : master’s thesis

Ovaj rad prikazuje rezultate terenskog mjerenja energije drobljenja na eksploatacijskom polju „Očura“. Hipoteza rada je da smanjenjem veličine čestica raste energija potrebna za njihovo sitnjenje. Na separacijskom postrojenju eksploatacijskog polja „Očura“ uzorci su drobljeni u čeljusnoj (primarnoj), konusnoj (sekundarnoj) i udarnoj (tercijarnoj) drobilici. Pomoću mjernog sustava mjerena je potrošnja električne energije elektromotora prilikom drobljenja u pojedinim drobilicama. U čeljusnoj drobilici izdrobljeno je 16 pojedinačnih uzoraka te je određivana njihova specifična energija. U konusnoj i udarnoj drobilici izdrobljen je materijal iz čeljusne drobilice, ali odjednom. Uspoređivana je specifična energija drobljenja u čeljusnoj, konusnoj i udarnoj drobilici. Statističkom analizom utvrđivana je ovisnost između mase uzorka, specifičnoj energiji drobljenja, prosječnoj snazi drobljenja i maksimalnoj snazi tijekom drobljenja.This thesis shows the results of crushing energy measurements on the field on „Očura“ surface mine. The hypothesis of the thesis is that lowering the particle size raises the energy needed for their comminution. Samples of rock were crushed in jaw (primary), cone (secondary) and impact (tertiary) crushers on the „Očura“ processing plant. Electrical energy consumption of the crushers motor was measured with the measuring system during sample crushing. In the jaw crusher, 16 individual samples were crushed and their specific crushing energy was calculated. In the cone and impact crushers the material form the jaw crusher was crushed all at once. Specific crushing energy of jaw, cone and impact crushers was compared. Dependence between samples mass, specific crushing energy, average crushing power and maximum crushing power was determined by statiscial data processing

Crushing energy measurements on the field : master’s thesis

Ovaj rad prikazuje rezultate terenskog mjerenja energije drobljenja na eksploatacijskom polju „Očura“. Hipoteza rada je da smanjenjem veličine čestica raste energija potrebna za njihovo sitnjenje. Na separacijskom postrojenju eksploatacijskog polja „Očura“ uzorci su drobljeni u čeljusnoj (primarnoj), konusnoj (sekundarnoj) i udarnoj (tercijarnoj) drobilici. Pomoću mjernog sustava mjerena je potrošnja električne energije elektromotora prilikom drobljenja u pojedinim drobilicama. U čeljusnoj drobilici izdrobljeno je 16 pojedinačnih uzoraka te je određivana njihova specifična energija. U konusnoj i udarnoj drobilici izdrobljen je materijal iz čeljusne drobilice, ali odjednom. Uspoređivana je specifična energija drobljenja u čeljusnoj, konusnoj i udarnoj drobilici. Statističkom analizom utvrđivana je ovisnost između mase uzorka, specifičnoj energiji drobljenja, prosječnoj snazi drobljenja i maksimalnoj snazi tijekom drobljenja.This thesis shows the results of crushing energy measurements on the field on „Očura“ surface mine. The hypothesis of the thesis is that lowering the particle size raises the energy needed for their comminution. Samples of rock were crushed in jaw (primary), cone (secondary) and impact (tertiary) crushers on the „Očura“ processing plant. Electrical energy consumption of the crushers motor was measured with the measuring system during sample crushing. In the jaw crusher, 16 individual samples were crushed and their specific crushing energy was calculated. In the cone and impact crushers the material form the jaw crusher was crushed all at once. Specific crushing energy of jaw, cone and impact crushers was compared. Dependence between samples mass, specific crushing energy, average crushing power and maximum crushing power was determined by statiscial data processing

Razlike u funkcionalnom pokretu između atletičara bacača, skakača i sprintera

Glavni cilj ovog rada je utvrditi da li postoje razlike u funkcionalnom pokretu između atletičara bacača, skakača i sprintera na uzorku od 54 atletičarke i atletičara (17 – 34 godine, 19 Ž i 35 M) na području grada Zagreba. Za potrebe ovog istraživanja korišteno je 7 testova iz FMS metodologije s ciljem utvrđivanja trenutnog stanja funkcionalnog pokreta. Mann – Whitney U - test je potvrdio statistički značajnu razliku u testu prekorak između atletičara bacača i skakača u kojem su atletičari skakači pokazali značajno više rezultate od atletičara bacača. Uzrok tome može biti veća stabilnost koraka i pokretljivost kukova u sagitalnoj ravnini koju više zahtijevaju tehnike skokova nego tehnike bacanja u atletici. Velik broj ponavljanja jednakih kretnih struktura jednom rukom, nogom i stranom tijela je češći kod atletičara bacača, što može dovesti do razvoja asimetrija u lokomotornom sustavu, te posljedično niže ocjene u testu prekorak.Athletics is one of the most popular sports in the world. It contains running, jumping, throwing and combined events. The aim of this study was to assess differences in functional movement between throwers, sprinters and jumpers (n=54, 17-34 years). The Functional Movement Screen (FMSTM) was used to assess functional movement in seven fundamental movement patterns. The study showed that a significant difference between throwers and jumpers exists only in one functional movement pattern (hurdle step), but not in other FMS tests. This difference in FMS results can be explained with higher demand of postural stability and hip mobility in sagittal plane which is more frequent in the jumpers' events and trainings then in throwers'. The results of the study need to be considered while implementing data into practical usage and while using FMS as a diagnostic tool among athletes in athletics

GRIMGEP: Learning Progress for Robust Goal Sampling in Visual Deep Reinforcement Learning

Designing agents, capable of learning autonomously a wide range of skills is critical in order to increase the scope of reinforcement learning. It will both increase the diversity of learned skills and reduce the burden of manually designing reward functions for each skill. Self-supervised agents, setting their own goals, and trying to maximize the diversity of those goals have shown great promise towards this end. However, a currently known limitation of agents trying to maximize the diversity of sampled goals is that they tend to get attracted to noise or more generally to parts of the environments that cannot be controlled (distractors). When agents have access to predefined goal features or expert knowledge, absolute Learning Progress (ALP) provides a way to distinguish between regions that can be controlled and those that cannot. However, those methods often fall short when the agents are only provided with raw sensory inputs such as images. In this work we extend those concepts to unsupervised image-based goal exploration. We propose a framework that allows agents to autonomously identify and ignore noisy distracting regions while searching for novelty in the learnable regions to both improve overall performance and avoid catastrophic forgetting. Our framework can be combined with any state-of-the-art novelty seeking goal exploration approaches. We construct a rich 3D image based environment with distractors. Experiments on this environment show that agents using our framework successfully identify interesting regions of the environment, resulting in drastically improved performances. The source code is available at https://sites.google.com/view/grimgep

Konvergencija cikličke Jacobijeve metode za hermitsku matricu reda 4

U ovom radu prikazali smo Jacobijevu metodu za hermitske matrice reda 4 definiranu općom cikličkom pivotnom strategijom. Uveli smo relacije ekvivalencije \sim, \underaccent{\tilde}{s}, \underaccent{\tilde}{w}, \underaccent{\tilde}{p} na skupu svih cikličkih strategija te pokazali da konvergenost metode pod nekom strategijom povlači konvergentnost metode pod njoj ekvivalentnom strategijom. Zatim smo pokazali globalnu konvergenciju metode pod strategijama iz specijalne familije $C_1$ te pod jednom paralelnom strategijom. Pomoću računalnog programa podijelili smo 720 cikličkih strategija u 5 klasa ekvivalencije, te u svakoj klasi pronašli strategiju za koju smo pokazali globalnu konvergenciju. To je bilo dovoljno da se pokaže globalna konvergencija metode pod svih 720 cikličkih strategija.In this work we have presented the Jacobi method for Hermitian matrices of order 4 defined by a general cyclic pivot strategy. We have introduced equivalence relations \sim, \underaccent{\tilde}{s}, \underaccent{\tilde}{w}, \underaccent{\tilde}{p} on the set of cyclic strategies and shown that convergence of the method under some strategy implies convergence of the method under an equivalent strategy. Then we have shown the global convergence of the method under the strategies from the special family $C_1$ and under one parallel strategy. Using a computer program, we have partitioned the set of 720 cyclic strategies in 5 equivalence classes. For each class we have found a strategy for which the method is convergent. That is enough to show the global convergence of the method under all 720 cyclic strategies