Not So SuperDense Coding - Deterministic Dense Coding with Partially Entangled States

The utilization of a $d$-level partially entangled state, shared by two parties wishing to communicate classical information without errors over a noiseless quantum channel, is discussed. We analytically construct deterministic dense coding schemes for certain classes of non-maximally entangled states, and numerically obtain schemes in the general case. We study the dependency of the information capacity of such schemes on the partially entangled state shared by the two parties. Surprisingly, for $d>2$ it is possible to have deterministic dense coding with less than one ebit. In this case the number of alphabet letters that can be communicated by a single particle, is between $d$ and 2d. In general we show that the alphabet size grows in "steps" with the possible values $d, d+1, ..., d^2-2$. We also find that states with less entanglement can have greater communication capacity than other more entangled states.Comment: 6 pages, 2 figures, submitted to Phys. Rev.

Counting Hyperbolic Manifolds

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Deterministic and Probabilistic Binary Search in Graphs

We consider the following natural generalization of Binary Search: in a given undirected, positively weighted graph, one vertex is a target. The algorithm's task is to identify the target by adaptively querying vertices. In response to querying a node $q$, the algorithm learns either that $q$ is the target, or is given an edge out of $q$ that lies on a shortest path from $q$ to the target. We study this problem in a general noisy model in which each query independently receives a correct answer with probability $p > \frac{1}{2}$ (a known constant), and an (adversarial) incorrect one with probability $1-p$. Our main positive result is that when $p = 1$ (i.e., all answers are correct), $\log_2 n$ queries are always sufficient. For general $p$, we give an (almost information-theoretically optimal) algorithm that uses, in expectation, no more than $(1 - \delta)\frac{\log_2 n}{1 - H(p)} + o(\log n) + O(\log^2 (1/\delta))$ queries, and identifies the target correctly with probability at leas $1-\delta$. Here, $H(p) = -(p \log p + (1-p) \log(1-p))$ denotes the entropy. The first bound is achieved by the algorithm that iteratively queries a 1-median of the nodes not ruled out yet; the second bound by careful repeated invocations of a multiplicative weights algorithm. Even for $p = 1$, we show several hardness results for the problem of determining whether a target can be found using $K$ queries. Our upper bound of $\log_2 n$ implies a quasipolynomial-time algorithm for undirected connected graphs; we show that this is best-possible under the Strong Exponential Time Hypothesis (SETH). Furthermore, for directed graphs, or for undirected graphs with non-uniform node querying costs, the problem is PSPACE-complete. For a semi-adaptive version, in which one may query $r$ nodes each in $k$ rounds, we show membership in $\Sigma_{2k-1}$ in the polynomial hierarchy, and hardness for $\Sigma_{2k-5}$

Is Ductal Carcinoma In Situ With “Possible Invasion” More Predictive of Invasive Carcinoma Than Pure Ductal Carcinoma In Situ?

AbstractObjectivesTo compare the underestimation of ductal carcinoma in situ (DCIS) vs DCIS with “possible invasion” at breast biopsy and to determine if any factors related to clinical indication, imaging abnormality, biopsy, or DCIS-grade affected the likelihood of underestimation.MethodsOf 3836 consecutive lesions that were biopsied by using a 14-gauge needle, 117 lesions revealed DCIS. Surgical pathology results of invasive carcinoma were compared with needle biopsy results of DCIS or DCIS with possible invasion. Clinical indication, imaging abnormality, biopsy guidance modality, sample number, and histologic grade were recorded. Yates corrected χ2 and Fisher exact tests were used to determine differences between groups.ResultsA total of 101 lesions were DCIS and 16 were DCIS with possible invasion at biopsy. Thirty-six of 117 lesions (31%) revealed invasive carcinoma at resection pathology. Invasive carcinoma was present more often when DCIS with possible invasion was diagnosed compared with pure DCIS (7/16 [44%] vs 29/101 [29%], P = .36). No factor, including clinical indication, imaging abnormality, biopsy guidance method, sample number, or grade, was found to significantly affect the likelihood of underestimation for lesions diagnosed as DCIS vs DCIS with “possible invasion.” The likelihood of pure DCIS underestimation significantly increased when lesions were high grade compared with either intermediate or low grade (18/44 [41%] vs 9/44 [21%] vs 2/10 [20%], P = .03).ConclusionFor lesions biopsied by using a 14-gauge needle, there is a trend towards underestimation of the presence of invasive carcinoma when pathology reveals DCIS with possible invasion compared with pure DCIS. High-grade DCIS was significantly more likely to be underestimated

Legal Certainty in the Pawn Guarantee System in Indonesia in Anticipation of Opportunities and Challenges of Global Economic Competition

The Credit system with guarantee pledge long has its roots in public life in Indonesia based on settings in the KUH Perdata article 1150. Advantages of the credit system with the pawn lies in a simple procedure and based on the principle of inbezet stelling who controlled goods are considered as owner. In the development system pawn shops especially with modern business, trends start in doubt because of suspicions about pawn shops as holding “barang tada” (stolen). This weakness appears due to legal certainty in the pawn guarantee system in Indonesia is related to the responsibility of PT Pegadaian Indonesia, against the pawn shops and the dispute resolution system. It became the focused of the problem in this research by using the methods of normative legal research found that interest in system pawn shops quite high in Indonesia. The fundamental weakness of the system has not been applied to pawn shops customer recognition system it must be addressed in improving public confidence towards the pawn shops to be able to compete with other financial institutions in globalization. Keywords: pawn, guarantee, legal certaint

Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and Minor-Free Graphs

A (1 + eps)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The most relevant measures for a distance-oracle construction are: space, query time, and preprocessing time. There are strong distance-oracle constructions known for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs (Abraham and Gavoille, PODC'06). However, these require Omega(eps^{-1} n lg n) space for n-node graphs. We argue that a very low space requirement is essential. Since modern computer architectures involve hierarchical memory (caches, primary memory, secondary memory), a high memory requirement in effect may greatly increase the actual running time. Moreover, we would like data structures that can be deployed on small mobile devices, such as handhelds, which have relatively small primary memory. In this paper, for planar graphs, bounded-genus graphs, and minor-excluded graphs we give distance-oracle constructions that require only O(n) space. The big O hides only a fixed constant, independent of \epsilon and independent of genus or size of an excluded minor. The preprocessing times for our distance oracle are also faster than those for the previously known constructions. For planar graphs, the preprocessing time is O(n lg^2 n). However, our constructions have slower query times. For planar graphs, the query time is O(eps^{-2} lg^2 n). For our linear-space results, we can in fact ensure, for any delta > 0, that the space required is only 1 + delta times the space required just to represent the graph itself

Large Language Models respond to Influence like Humans

Two studies tested the hypothesis that a Large Language Model (LLM) can be used to model psychological change following exposure to influential input. The first study tested a generic mode of influence - the Illusory Truth Effect (ITE) - where earlier exposure to a statement boosts a later truthfulness test rating. Analysis of newly collected data from human and LLM-simulated subjects (1000 of each) showed the same pattern of effects in both populations; although with greater per statement variability for the LLM. The second study concerns a specific mode of influence – populist framing of news to increase its persuasion and political mobilization. Newly collected data from simulated subjects was compared to previously published data from a 15-country experiment on 7286 human participants. Several effects from the human study were replicated by the simulated study, including ones that surprised the authors of the human study by contradicting their theoretical expectations; but some significant relationships found in human data were not present in the LLM data. Together the two studies support the view that LLMs have potential to act as models of the effect of influence

Interobserver Agreement for Endometrial Cancer Characteristics Evaluated on Biopsy Material

A shift toward a disease-based therapy designed according to patterns of failure and likelihood of nodal involvement predicted by pathologic determinants has recently led to considering a selective approach to lymphadenectomy for endometrial cancer. Therefore, it became critical to examine reproducibility of diagnosing the key determinants of risk, on preoperative endometrial tissue samples as well as the concordance between preoperative and postresection specimens. Six gynaecologic pathologists assessed 105 consecutive endometrial biopsies originally reported as positive for endometrial cancer for cell type (endometrioid versus nonendometrioid), tumor grade (FIGO 3-tiered and 2-tiered), nuclear grade, and risk category (low risk defined as endometrioid histology, grade 1 + 2 and nuclear grade <3). Interrater agreement levels were substantial for identification of nonendometrioid histology (κ = 0.63; SE = 0.025), high tumor grade (κ = 0.64; SE = 0.025), and risk category (κ = 0.66; SE = 0.025). The overall agreement was fair for nuclear grade (κ = 0.21; SE = 0.025). There is agreement amongst pathologists in identifying high-risk pathologic determinants on endometrial cancer biopsies, and these highly correlate with postresection specimens. This is ascertainment prerequisite adaptation of the paradigm shift in surgical staging of patients with endometrial cancer