Multiplicity of Closed Reeb Orbits on Prequantization Bundles

We establish multiplicity results for geometrically distinct contractible closed Reeb orbits of non-degenerate contact forms on a broad class of prequantization bundles. The results hold under certain index requirements on the contact form and are sharp for unit cotangent bundles of CROSS's. In particular, we generalize and put in the symplectic-topological context a theorem of Duan, Liu, Long, and Wang for the standard contact sphere. We also prove similar results for non-hyperbolic contractible closed orbits and briefly touch upon the multiplicity problem for degenerate forms. On the combinatorial side of the question, we revisit and reprove the enhanced common jump theorem of Duan, Long and Wang, and interpret it as an index recurrence result.Comment: 31 page

Simple vs complex temporal recurrences for video saliency prediction

This paper investigates modifying an existing neural network architecture for static saliency prediction using two types of recurrences that integrate information from the temporal domain. The first modification is the addition of a ConvLSTM within the architecture, while the second is a conceptually simple exponential moving average of an internal convolutional state. We use weights pre-trained on the SALICON dataset and fine-tune our model on DHF1K. Our results show that both modifications achieve state-of-the-art results and produce similar saliency maps. Source code is available at https://git.io/fjPiB

Relativnost pojma ren (človečnost): Ponovna raziskava odsekov 2A6 in 6A6 knjige Mencij s perspektive izkušenjske samointrospekcije

A textual difference exists between 2A6 and 6A6 of the Mengzi: In 2A6, the heart-mind of ceyin (compassion), xiuwu (shame), cirang (courtesy and modesty), and shifei (moral judgement) are said to be the four “duan” (germs) of ren (humaneness), yi (optimal appropriateness), li (observance of the rites), and zhi (wisdom), whereas in 6A6, the term “duan” is not found. For this reason, some scholars today criticize the interpretation that translates “duan” as “starting point”, which implies a substantial difference between the four germs and ren, yi, li, and zhi that apparently does not exist in 6A6. Instead, these scholars prefer another interpretation that takes “duan” as an indication of the essential sameness between the four germs and ren, yi, li, and zhi that are originally possessed by a morally perfect heart-mind. This essay re-evaluates these two interpretations. First, it argues that compared to the first, the second interpretation’s argument for a morally perfect heart-mind is less compatible with the nature of Mengzi’s moral philosophy as a teaching that focuses on self-introspection and moral cultivation in experience. Second, this essay reinforces the first interpretation by demonstrating the existence of two different senses of ren (as well as yi, li, and zhi) in the Mengzi, thus allowing it to coherently suggest that the heart-mind possessing the four germs as innate moral feelings is the same as the “relatively antecedent” ren, which is, at the same time, the starting point for developing the “relatively consequent” ren that is substantially different from the former.Med odsekoma 2A6 in 6A6 knjige Mencij je naslednja tekstualna razlika: V odseku 2A6 je srce-razum, ki goji ceyin (sočutje), xiuwu (sram), cirang (vljudnost in zmernost) in shifei (moralno presojo), obravnavan kot štiri »duan« (kali) vrlin, tj. ren (človečnost), yi (optimalna primernost), li (upoštevanje obredov) in zhi (modrost). V odseku 6A6 pa pojma »duan« ni mogoče najti. Zato danes nekateri strokovnjaki kritizirajo interpretacijo, v kateri je pojem »duan« preveden kot »izhodišče«, kar implicira bistveno razliko med štirimi kalmi ter ren, yi, li in zhi, ki pa v 6A6 očitno ne obstaja. Namesto tega so ti strokovnjaki veliko bolj naklonjeni razlagi, po kateri je »duan« označba za bistveno enakost štirih kali ter ren, yi, li in zhi, ki jih izvorno poseduje moralno izpopolnjen srce-razum. Ta esej ponovno ovrednoti ti dve interpretaciji. Prvič, članek zagovarja stališče, da je v primerjavi s prvo argument druge razlage za moralno popoln srce-razum manj skladen z naravo Mencijeve moralne filozofije kot nauka, ki se osredotoča na izkušenjsko samointrospekcijo in moralno kultivacijo. Drugič, ta esej podpre drugo razlago s ponazoritvijo obstoja dveh različnih pomenov pojma ren (kot tudi yi, li in zhi) v delu Mencij. S tem pa dopušča, da ta koherentno kaže, da je srce-razum, ki poseduje štiri kali kot ponotranjena moralna občutja, enak »relativno predhodni« vrlini ren in je hkrati izhodiščna točka razvoja »relativno posledične« ren, ki pa se občutno razlikuje od prejšnje

An Improved Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market

We present an improved combinatorial algorithm for the computation of equilibrium prices in the linear Arrow-Debreu model. For a market with $n$ agents and integral utilities bounded by $U$, the algorithm runs in $O(n^7 \log^3 (nU))$ time. This improves upon the previously best algorithm of Ye by a factor of \tOmega(n). The algorithm refines the algorithm described by Duan and Mehlhorn and improves it by a factor of \tOmega(n^3). The improvement comes from a better understanding of the iterative price adjustment process, the improved balanced flow computation for nondegenerate instances, and a novel perturbation technique for achieving nondegeneracy.Comment: to appear in SODA 201

Modelling of hydrothermal fluid compositions in the crust and upper mantle

Carbon-oxygen-hydrogen (COH) fluids are integral to the formation of many hydrothermal ore deposits (including orogenic gold, graphite), and diamond. Typically, a crustal/upper mantle COH fluid comprises H2O, CO2, CH4, H2, CO, C2H6, and O2. Crustal and upper mantle fluid compositions are constrained by pressure, temperature and redox state, and can be calculated if: (1) A reliable equation of state for fluid mixtures is available for the relevant pressure-temperature conditions is available for the calculation of fugacity coefficients; (2) Reliable thermodynamic variables including enthalpy, entropy and isobaric heat capacity can be obtained. Here, we used the equation of state by Zhang and Duan (2009) in conjunction with the NIST reference dataset to develop a user-friendly Excel spread sheet that allows the calculation of fluid compositions for a pressure-temperature range of > 0.5 kbar and 300-1500°C, respectively. Data manipulation and modelling was achieved with a combination of VBA, Python and SQL scripting and allowed us to validate the model calculations in the Excel spread sheet. Here, we used the equation of state by Zhang and Duan (2009) in conjunction with the NIST reference dataset to develop a user-friendly Excel spread sheet that allows the calculation of fluid compositions for a pressure-temperature range of > 0.5 kbar and 300-1500°C, respectively. Data manipulation and modelling was achieved with a combination of VBA, Python and SQL scripting and allowed us to validate the model calculations in the Excel spread sheet