Dynamics and Topology of S-gap Shifts

Let $S=\{s_i\in\mathbb N\cup\{0\}:0\leq s_i<s_{i+1}\}$ and let $d_{0}=s_{0}$ and $\Delta(S)=\{d_{n}\}_{n}$ where $d_{n}=s_{n}-s_{n-1}$. In this note, we show that an $S$-gap shift is subshift of finite type (SFT) if and only if $S$ is finite or cofinite, is almost-finite-type (AFT) if and only if $\Delta(S)$ is eventually constant and is sofic if and only if $\Delta(S)$ is eventually periodic. We also show that there is a one-to-one correspondence between the set of all $S$-gap shifts and $\{r \in \mathbb R: r \geq 0\}\backslash \{\frac{1}{n}: n \in {\mathbb N}\}$ up to conjugacy. This enables us to induce a topology and measure structure on the set of all $S$-gaps. By using this, we give the frequency of certain $S$-gap shifts with respect to their dynamical properties.Comment: This paper has been withdrawn due to a flaw in Theorem 3.2. The correct version with some minor results will be replace

Computations on Sofic S-gap Shifts

Let $S=\{s_{n}\}$ be an increasing finite or infinite subset of $\mathbb N \bigcup \{0\}$ and $X(S)$ the $S$-gap shift associated to $S$. Let $f_{S}(x)=1-\sum\frac{1}{x^{s_{n}+1}}$ be the entropy function which will be vanished at $2^{h(X(S))}$ where $h(X(S))$ is the entropy of the system. Suppose $X(S)$ is sofic with adjacency matrix $A$ and the characteristic polynomial $\chi_{A}$. Then for some rational function $Q_{S}$, $\chi_{A}(x)=Q_{S}(x)f_{S}(x)$. This $Q_{S}$ will be explicitly determined. We will show that $\zeta(t)=\frac{1}{f_{S}(t^{-1})}$ or $\zeta(t)=\frac{1}{(1-t)f_{S}(t^{-1})}$ when $|S|<\infty$ or $|S|=\infty$ respectively. Here $\zeta$ is the zeta function of $X(S)$. We will also compute the Bowen-Franks groups of a sofic $S$-gap shift.Comment: This paper has been withdrawn due to extending results about SFT shifts to sofic shifts (Theorem 2.3). This forces to apply some minor changes in the organization of the paper. This paper has been withdrawn due to a flaw in the description of the adjacency matrix (2.3

Single high-dose buprenorphine for opioid craving during withdrawal.

BackgroundOpioid use disorder is one of the most prevalent addiction problems worldwide. Buprenorphine is used as a medication to treat this disorder, but in countries where buprenorphine is unavailable in combination with naloxone, diversion can be a problem if the medication is given outside a hospital setting.ObjectiveThe objective of this research is to evaluate the effect of a single, high dose of buprenorphine on craving in opioid-dependent patients over 5 days of abstinence from use of other opioids. The primary goal was to determine the safety and efficacy of buprenorphine during withdrawal in a hospital setting.MethodsNinety men who used opium, heroin, or prescribed opioids and met DSM-5 criteria for opioid use disorder (severe form) were randomized to three groups (n = 30 per group) to receive a single, sublingual dose of buprenorphine (32, 64, or 96 mg). The study was conducted in an inpatient psychiatric ward, with appropriate precautions and monitoring of respiratory and cardiovascular measures. Buprenorphine was administered when the patients were in moderate opiate withdrawal, as indicated by the presence of four to five symptoms. A structured clinical interview was conducted, and urine toxicology testing was performed at baseline. Self-reports of craving were obtained at baseline and on each of the 5 days after buprenorphine administration.FindingsCraving decreased from baseline in each of the three groups (p &lt; 0.0001), with a significant interaction between group and time (p &lt; 0.038), indicating that groups with higher doses of buprenorphine had greater reduction.ConclusionsA single, high dose of buprenorphine can reduce craving during opioid withdrawal; additional studies with follow-up are warranted to evaluate safety

Safe Policy Synthesis in Multi-Agent POMDPs via Discrete-Time Barrier Functions

A multi-agent partially observable Markov decision process (MPOMDP) is a modeling paradigm used for high-level planning of heterogeneous autonomous agents subject to uncertainty and partial observation. Despite their modeling efficiency, MPOMDPs have not received significant attention in safety-critical settings. In this paper, we use barrier functions to design policies for MPOMDPs that ensure safety. Notably, our method does not rely on discretization of the belief space, or finite memory. To this end, we formulate sufficient and necessary conditions for the safety of a given set based on discrete-time barrier functions (DTBFs) and we demonstrate that our formulation also allows for Boolean compositions of DTBFs for representing more complicated safe sets. We show that the proposed method can be implemented online by a sequence of one-step greedy algorithms as a standalone safe controller or as a safety-filter given a nominal planning policy. We illustrate the efficiency of the proposed methodology based on DTBFs using a high-fidelity simulation of heterogeneous robots.Comment: 8 pages and 4 figure

Barrier Functions for Multiagent-POMDPs with DTL Specifications

Multi-agent partially observable Markov decision processes (MPOMDPs) provide a framework to represent heterogeneous autonomous agents subject to uncertainty and partial observation. In this paper, given a nominal policy provided by a human operator or a conventional planning method, we propose a technique based on barrier functions to design a minimally interfering safety-shield ensuring satisfaction of high-level specifications in terms of linear distribution temporal logic (LDTL). To this end, we use sufficient and necessary conditions for the invariance of a given set based on discrete-time barrier functions (DTBFs) and formulate sufficient conditions for finite time DTBF to study finite time convergence to a set. We then show that different LDTL mission/safety specifications can be cast as a set of invariance or finite time reachability problems. We demonstrate that the proposed method for safety-shield synthesis can be implemented online by a sequence of one-step greedy algorithms. We demonstrate the efficacy of the proposed method using experiments involving a team of robots

“Quo Vadis Infotainment”?

According to Marshall McLuhan, the world has become a global village where modern communication media opened up unlimited interactions among people all over the world. Among other things, mass communication channel has rapidly developed, allowing greater mass of information transmissions to be spread for all members of society in no time. Unfortunately, the rapid development of mass media was not followed by better quality in terms of media content. Infotainments were everywhere, offering latest report concerning celebrity news in detail, and raising serious questions concerning ethics, privacy, public policy, and news quality today