Decision Trees, Protocols, and the Fourier Entropy-Influence Conjecture

Given $f:\{-1, 1\}^n \rightarrow \{-1, 1\}$, define the \emph{spectral distribution} of $f$ to be the distribution on subsets of $[n]$ in which the set $S$ is sampled with probability $\widehat{f}(S)^2$. Then the Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai (1996) states that there is some absolute constant $C$ such that $\operatorname{H}[\widehat{f}^2] \leq C\cdot\operatorname{Inf}[f]$. Here, $\operatorname{H}[\widehat{f}^2]$ denotes the Shannon entropy of $f$'s spectral distribution, and $\operatorname{Inf}[f]$ is the total influence of $f$. This conjecture is one of the major open problems in the analysis of Boolean functions, and settling it would have several interesting consequences. Previous results on the FEI conjecture have been largely through direct calculation. In this paper we study a natural interpretation of the conjecture, which states that there exists a communication protocol which, given subset $S$ of $[n]$ distributed as $\widehat{f}^2$, can communicate the value of $S$ using at most $C\cdot\operatorname{Inf}[f]$ bits in expectation. Using this interpretation, we are able show the following results: 1. First, if $f$ is computable by a read-$k$ decision tree, then $\operatorname{H}[\widehat{f}^2] \leq 9k\cdot \operatorname{Inf}[f]$. 2. Next, if $f$ has $\operatorname{Inf}[f] \geq 1$ and is computable by a decision tree with expected depth $d$, then $\operatorname{H}[\widehat{f}^2] \leq 12d\cdot \operatorname{Inf}[f]$. 3. Finally, we give a new proof of the main theorem of O'Donnell and Tan (ICALP 2013), i.e. that their FEI$^+$ conjecture composes. In addition, we show that natural improvements to our decision tree results would be sufficient to prove the FEI conjecture in its entirety. We believe that our methods give more illuminating proofs than previous results about the FEI conjecture

Pilot interaction with automated airborne decision making systems

The current research is focused on detection of human error and protection from its consequences. A program for monitoring pilot error by comparing pilot actions to a script was described. It dealt primarily with routine errors (slips) that occurred during checklist activity. The model to which operator actions were compared was a script. Current research is an extension along these two dimensions. The ORS fault detection aid uses a sophisticated device model rather than a script. The newer initiative, the model-based and constraint-based warning system, uses an even more sophisticated device model and is to prevent all types of error, not just slips or bad decision

Overcoming the shadow and achieving individuation through a Hero's journey in Tunku Halim's "A Sister's Tale"

In Jungian psychology, Individuation is the process of achieving psychological maturation wherein individuals are able to integrate their conscious and unconscious mind to create a balanced psyche. One aspect of the unconscious mind that needs to be integrated with the conscious is the Shadow, a psychological component consisting of all rejected and repressed aspects of one's personality. The process of dealing with the Shadow aspect is analogous to the journey of the Hero archetype, and the goal of this journey is Individuation, whereby one becomes connected to their Self, an archetype that represents wholeness and totality. In Tunku Halim's "A Sister's Tale" (1999), Jessica has been pulled into a Hero's journey because of an unaddressed repressed guilt that ultimately becomes her Shadow. This paper aims to examine Jessica's Heroic journey in attaining her Self through the integration of her unconscious component, the Shadow, with her consciousness. To achieve this objective, the text is analysed through Jungian's concept of the Shadow and Hero archetypes. The findings reveal that Jessica's Shadow had become too dense for a successful integration to occur and therefore, she failed to achieve Individuation

Suppressed Andreev Reflection at the Normal-Metal / Heavy-Fermion Superconductor CeCoIn5_5 Interface

Dynamic conductance spectra are taken from Au/CeCoIn$_5$ point contacts in the Sharvin limit along the (001) and (110) directions. Our conductance spectra, reproducibly obtained over wide ranges of temperature, constitute the cleanest data sets ever reported for HFSs. A signature for the emerging heavy-fermion liquid is evidenced by the development of the asymmetry in the background in the normal state. Below $T_c$, an enhancement of the sub-gap conductance arising from Andreev reflection is observed, with the magnitude of $\sim$ 13.3 % and $\sim$ 11.8 % for the (001) and the (110) point contacts, respectively, an order of magnitude smaller than those observed in conventional superconductors but consistent with those in other HFSs. Our zero-bias conductance data for the (001) point contacts are best fit with the extended BTK model using the d-wave order parameter. The fit to the full conductance curve of the (001) point contact indicates the strong coupling nature ($2\Delta/k_{B}T_c = 4.64$). However, our observed suppression of both the Andreev reflection signal and the energy gap indicates the failure of existing models. We provide possible directions for theoretical formulations of the electronic transport across an N/HFS interface. Several qualitative features observed in the (110) point contacts provide the first clear spectroscopic evidence for the $d_{x^2-y^2}$ symmetry.Comment: 13 pages, 7 figures, LaTeX, paper invited and submitted to SPIE Conference on Strongly Correlated Electron Materials: Physics and Nanoengineering, in San Diego, California, July 31 - August 4, 200

Vision based Object Recognition of E-Puck Mobile Robot for Warehouse Application

At present, most warehouses still require human services for unloading of goods. Unloading of goods requires a continuous system to ensure the quality of work productivity. Therefore the need of autonomous robot system in warehouse is needed to improve the quality of work. Thus, a localization and recognition algorithm is developed and implemented on the E-puck robot. The task involves the recognition of desired object based on their colour (red and blue) and locating the desired object to the target location (marked by green marker). In addition, the collision avoidance algorithm is also developed and integrated to allow the robot manoeuvre safely in its working environment. The colour histogram technique is used to recognize the desired object and the target location. Based on the experimental results, the developed algorithm is successfully fulfilling the pick and place requirement with success rate of approximately 70% in simulation study and 50% in real implementation

Algorithms for computing lengths of chains in integral partition lattices

AbstractLet Pl,n denote the partition lattice of l with n parts, ordered by Hardy–Littlewood–Polya majorization. For any two comparable elements x and y of Pl,n, we denote by M(x,y), m(x,y), f(x,y), and F(x,y), respectively, the sizes of four typical chains between x and y: the longest chain, the shortest chain, the lexicographic chain, and the counter-lexicographic chain. The covers u=(u1,…,un)≻v=(v1,…,vn) in Pl,n are of two types: N-shift (nearby shift) where vi=ui−1, vi+1=ui+1+1 for some i; and D-shift (distant shift) where ui−1=vi=vi+1=⋯=vj=uj+1 for some i and j. An N-shift (a D-shift) is pure if it is not a D-shift (an N-shift). We develop linear algorithms for calculating M(x,y), m(x,y), f(x,y), and F(x,y), using the leftmost pure N-shift first search, the rightmost pure D-shift first search, the leftmost N-shift first search, and the rightmost D-shift first search, respectively. Those algorithms have significant applications in complexity analysis of biological sequences