Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes

Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on bits transmitted per second. A decoder uses the received codewords to causally estimate the process in real time. The encoder and the decoder are synchronized in time. We aim to find the optimal encoding and decoding policies that minimize the end-to-end estimation mean-square error under the rate constraint. For a class of continuous Markov processes satisfying regularity conditions, we show that the optimal encoding policy transmits a 1-bit codeword once the process innovation passes one of two thresholds. The optimal decoder noiselessly recovers the last sample from the 1-bit codewords and codeword-generating time stamps, and uses it as the running estimate of the current process, until the next codeword arrives. In particular, we show the optimal causal code for the Ornstein-Uhlenbeck process and calculate its distortion-rate function

Optimal Causal Rate-Constrained Sampling of the Wiener Process

We consider the following communication scenario. An encoder causally observes the Wiener process and decides when and what to transmit about it. A decoder makes real-time estimation of the process using causally received codewords. We determine the causal encoding and decoding policies that jointly minimize the mean-square estimation error, under the long-term communication rate constraint of R bits per second. We show that an optimal encoding policy can be implemented as a causal sampling policy followed by a causal compressing policy. We prove that the optimal encoding policy samples the Wiener process once the innovation passes either √(1/R) or −√(1/R), and compresses the sign of the innovation (SOI) using a 1-bit codeword. The SOI coding scheme achieves the operational distortion-rate function, which is equal to D^(op)(R)=1/(6R). Surprisingly, this is significantly better than the distortion-rate tradeoff achieved in the limit of infinite delay by the best non-causal code. This is because the SOI coding scheme leverages the free timing information supplied by the zero-delay channel between the encoder and the decoder. The key to unlock that gain is the event-triggered nature of the SOI sampling policy. In contrast, the distortion-rate tradeoffs achieved with deterministic sampling policies are much worse: we prove that the causal informational distortion-rate function in that scenario is as high as D_(DET)(R)=5/(6R). It is achieved by the uniform sampling policy with the sampling interval 1/R. In either case, the optimal strategy is to sample the process as fast as possible and to transmit 1-bit codewords to the decoder without delay

Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes

Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on bits transmitted per second. A decoder uses the received codewords to causally estimate the process in real time. The encoder and the decoder are synchronized in time. We aim to find the optimal encoding and decoding policies that minimize the end-to-end estimation mean-square error under the rate constraint. For a class of continuous Markov processes satisfying regularity conditions, we show that the optimal encoding policy transmits a 1-bit codeword once the process innovation passes one of two thresholds. The optimal decoder noiselessly recovers the last sample from the 1-bit codewords and codeword-generating time stamps, and uses it as the running estimate of the current process, until the next codeword arrives. In particular, we show the optimal causal code for the Ornstein-Uhlenbeck process and calculate its distortion-rate function

Effect of model race and viewing perspective on body attractiveness and body size assessment in young Caucasian women: an eye-tracking study

Research has indicated that Caucasian women gaze more often at waist–hip and chest regions than other local body areas when assessing female body attractiveness and body size, and this stereotypical gaze distribution is further modulated by their own body satisfaction and body composition. However, little is known whether the model race and viewing perspective could affect women’s body-viewing gaze behaviour and body perception. Here, we presented female body images of Caucasian, Asian and African avatars in a continuum of common dress sizes in full frontal, mid-profile and rear view, and asked young Caucasian women to rate the perceived body attractiveness and body size. Their body-viewing gaze distributions were then correlated with their behavioural responses, their own body composition and body satisfaction. Our analysis revealed a clear in-group favoritism, in which Caucasian women tended to rate Caucasian avatars more attractive and slimmer than Asian and African avatars. Their body-viewing gaze patterns, on the other hand, were not affected by avatar race but were modulated by viewing perspectives. The frontal-view body (especially upper-body and waist–hip regions) attracted the highest proportion of viewing time, followed by the mid-profile view and then the rear-view body. Furthermore, our participants’ own body composition and satisfaction level did not affect their judgement of other women’s body attractiveness and body size, but could influence their gaze allocation at local body features. It seems that both body perception and body-viewing gaze behaviour are subject to group and individual biases

Is Turkey Acting Fairly? -- Turkey's Choice in TLORAMIDS

Abstract: Since 1952, Turkey has formally committed to the US/NATO alliance and taken part in the collective defense system within the Alliance. However, in September 2013, Turkey made a surprise move and announced its intention to buy China's long-range missile defense system over the competitors' products including from NATO countries. Notably, the maker of the FD-2000 (HQ-9) is a state-owned company-China Precision Machinery Import and Export Corporation (CPMEIC), which is under American sanctions for transferring missile technology to the states opposed to the West and its allies. Due to the risk that China could access NATO's intelligence and military information across the region, Turkey's choice of the Chinese FD-2000 set off a massive controversy, raising NATO's suspicions about Turkey's intentions, which carries serious implications for Turkey's attempts to strengthen ties with China. This study aims to provide insights into Turkey's pursuit of an indigenous Long Range Missile Defense System (T-LORAMIDS), providing an evaluation focusing on three questions: What is Turkey's motivation in acquiring T-LORAMIDS? How does Turkey's realist behavior fit into its decision to purchase T-LORAMIDS? Will Turkey's choice of missile defense system eventually make its current intimate involvement with US/NATO redundant? The article's basic argument is that Turkey remains a staunch ally of the West, and its incongruous behavior may be explained and validated through analyzing its realpolitik approach and desire for strategic balance, which is perceived by Turkey as attempting to retain the advantage in managing strategic relations with its partners