Constant Distortion Research Articles

A face cover perspective to \(\ell_{1}\) embeddings of planar graphs

It was conjectured by Gupta et al. [Combinatorica04] that every planar graph can be embedded into \(\ell_{1}\) with constant distortion. However, given an \(n\) -vertex weighted planar graph, the best upper bound on the distortion is only \(O(\sqrt{\log n})\) , by Rao [SoCG99]. In this paper we study the case where there is a set \(K\) of terminals, and the goal is to embed only the terminals into \(\ell_{1}\) with low distortion. In a seminal paper, Okamura and Seymour [J.Comb.Theory81] showed that if all the terminals lie on a single face, they can be embedded isometrically into \(\ell_{1}\) . The more general case, where the set of terminals can be covered by \(\gamma\) faces, was studied by Lee and Sidiropoulos [STOC09] and Chekuri et al. [J.Comb.Theory13]. The state of the art is an upper bound of \(O(\log\gamma)\) by Krauthgamer, Lee and Rika [SODA19]. Our contribution is a further improvement on the upper bound to \(O(\sqrt{\log\gamma})\) . Since every planar graph has at most \(O(n)\) faces, any further improvement on this result, will be a major breakthrough, directly improving upon Rao's long standing upper bound. Moreover, it is well known that the flow-cut gap equals to the distortion of the best embedding into \(\ell_{1}\) . Therefore, our result provides a polynomial time \(O(\sqrt{\log\gamma})\) -approximation to the sparsest cut problem on planar graphs, for the case where all the demand pairs can be covered by \(\gamma\) faces.

Low-Distortion Clustering with Ordinal and Limited Cardinal Information

Motivated by recent work in computational social choice, we extend the metric distortion framework to clustering problems. Given a set of n agents located in an underlying metric space, our goal is to partition them into k clusters, optimizing some social cost objective. The metric space is defined by a distance function d between the agent locations. Information about d is available only implicitly via n rankings, through which each agent ranks all other agents in terms of their distance from her. Still, even though no cardinal information (i.e., the exact distance values) is available, we would like to evaluate clustering algorithms in terms of social cost objectives that are defined using d. This is done using the notion of distortion, which measures how far from optimality a clustering can be, taking into account all underlying metrics that are consistent with the ordinal information available. Unfortunately, the most important clustering objectives (e.g., those used in the well-known k-median and k-center problems) do not admit algorithms with finite distortion. To sidestep this disappointing fact, we follow two alternative approaches: We first explore whether resource augmentation can be beneficial. We consider algorithms that use more than k clusters but compare their social cost to that of the optimal k-clusterings. We show that using exponentially (in terms of k) many clusters, we can get low (constant or logarithmic) distortion for the k-center and k-median objectives. Interestingly, such an exponential blowup is shown to be necessary. More importantly, we explore whether limited cardinal information can be used to obtain better results. Somewhat surprisingly, for k-median and k-center, we show that a number of queries that is polynomial in k and only logarithmic in n (i.e., only sublinear in the number of agents for the most relevant scenarios in practice) is enough to get constant distortion.

Discoidin domain receptor-2 enhances secondary alveolar septation in mice by activating integrins and modifying focal adhesions.

The extracellular matrix (ECM) of the pulmonary parenchyma must maintain the structural relationships among resident cells during the constant distortion imposed by respiration. This dictates that both the ECM and cells adapt to changes in shape, while retaining their attachment. Membrane-associated integrins and discoidin domain receptors (DDR) bind collagen and transmit signals to the cellular cytoskeleton. Although the contributions of DDR2 to collagen deposition and remodeling during osseous development are evident, it is unclear how DDR2 contributes to lung development. Using mice (smallie, Slie/Slie, DDR2Δ) bearing a spontaneous inactivating deletion within the DDR2 coding region, we observed a decrease in gas-exchange surface area and enlargement of alveolar ducts. Compared with fibroblasts isolated from littermate controls, DDR2Δ fibroblasts, spread more slowly, developed fewer lamellipodia, and were less responsive to the rigidity of neighboring collagen fibers. Activated β1-integrin (CD29) was reduced in focal adhesions (FA) of DDR2Δ fibroblasts, less phospho-zyxin localized to and fewer FA developed over ventral actin stress fibers, and the adhesions had a lower aspect ratio compared with controls. However, DDR2 deletion did not reduce cellular displacement of the ECM. Our findings indicate that DDR2, in concert with collagen-binding β1-integrins, regulates the timing and location of focal adhesion formation and how lung fibroblasts respond to ECM rigidity. Reduced rigidity sensing and mechano-responsiveness may contribute to the distortion of alveolar ducts, where the fiber cable-network is enriched and tensile forces are concentrated. Strategies targeting DDR2 could help guide fibroblasts to locations where tensile forces organize parenchymal repair.

“. . .delivered from the lie of being truth”: The Affective Force of Disinformation, Stickiness and Dissensus in Randy Ribay’s Patron Saints of Nothing

Waged in 2016, Philippine President Rodrigo Duterte’s war on drugs has claimed over 20,000 lives according to human rights groups. The Duterte administration’s own count is significantly lower: around 6,000. The huge discrepancy between the government’s official count and that of arguably more impartial organizations about something as concretely material as body count is symptomatic of how disinformation is central to the Duterte administration and how it can sustain the approval of the majority of the Philippine electorate. We suggest that Duterte’s populist politics generates what Boler and Davis (2018) call “affective feedback loops,” which create emotional and informational ecosystems that facilitate smooth algorithmic governance. We turn to Patron Saints of Nothing, a recently published novel by Randy Ribay about a Filipino-American who goes back to the Philippines to uncover the truth behind the death of his cousin. Jay’s journey into the “heart of darkness” as a “hyphenated” individual (Filipino-American) allows him access to locally networked subjectivities but not its affective entanglements. Throughout the novel, he encounters numerous versions of the circumstances of Jun’s demise and the truth remains elusive at the end of the novel. We argue that despite the constant distortion of fact and fiction in the novel, what remains relatively stable or “sticky” throughout the novel are the letters from Jun Reguero that Jay carries with him back to the Philippines. We suggest that these letters can potentially serve as a form of “dissensus” that challenges the constant redistribution of the sensible in the novel.

Features of saliva diagnostics and threshold gustometry in patients with non-alcoholic fatty liver disease

Objective — to determine the features of dental complaints and the threshold of taste sensitivity of the tongue receptors to glucose in patients with non‑alcoholic fatty liver disease (NAFLD) against the background of insulin resistance.
 Materials and methods. The study included 65 patients (29 (44.6 %) women and 36 (55.4 %) men) with NAFLD (the main group) and 24 somatically healthy subjects. The mean body mass index was 36.4 kg/m2 in the main group, and 22.8 kg/m2 in the controls. All patients had insulin resistance (НОМА index — 8.0). Dental examinations included questionnaires of patients with complaints’ detailing, clinical examination of the oral cavity, study of salivation rate, determination of the sensitivity of the taste receptors of the tongue to glucose by the method of gustometry.
 Results. It has been established that the mostly frequent complaints of patients in the main group were constant dry mouth, taste distortion and halitosis. They demonstrated a decrease in salivation rate up to 0.24 ± 0.13 ml per minute, changes in the taste sensitivity of the tongue to sweet, that was several times higher than the threshold of the physiological norm. The strong direct correlation has been proved between oral dryness and salivation rate. Correlations of moderate strength were confirmed between the secretion rate and glucose concentration according to gustometry, and between taste distortion and halitosis.
 Conclusions. Almost 90 % of patients with non‑alcoholic fatty liver disease have typical dental complaints. Questioning patients on the main dental complaints, studying the parameters of the oral fluid and threshold gustometry are the modern, non‑invasive methods, enabling the control of the disease course and assessment of the treatment efficacy.

Hollywood, American Politics, and Terrorism: When Art Turns into a Political Tool

Since Sirocco, a 1951 film, the United States' cinema, Hollywood, has produced many terrorism films that have portrayed Arabs and Muslims unjustly as “terrorists.” After the 9/11 terrorist attacks, Hollywood's projection of prejudice and negative stereotypes of the Arabs and Muslims have been fostered. The post-9/11 period was an era in which the White House, the Pentagon, and the Central Intelligence Agency (CIA) contributed directly and indirectly to the production of several terrorism films. In Zero Dark Thirty, gifts were offered to some CIA agents in order to obtain classified information and various accesses. In Iron Man, funding and resources were provided, a green light was given, and strict regulations were imposed by the Pentagon to portray the military in a positive light. In Syriana, a CIA agent had a friendly relationship with the film screenwriter, and much of the film events were inspired by the agent's personal experiences. The post-9/11 films have been used to spread stereotyped demeaning images of the Arabs and Muslims and perpetuated a constant distortion of Muslim communities. They have therefore severely targeted Muslims and depicted them as murderers and criminals, who express the feeling of hatred towards Western civilization.

Reversible Data Hiding in JPEG Images Under Multi-Distortion Metric

Reversible Data Hiding (RDH) in JPEG images is valuable for many applications, such as archive management and image authentication. Recently, there emerged a lot of related works for JPEG RDH, however, the current methods utilize the histogram-shifting-based framework in a constant distortion metric, which does not consider the property of DCT coefficients whose modification distortion is miscellaneous with respect to DCT frequency. In this paper, we propose a novel JPEG RDH scheme under multi-distortion metric. At first, the modification distortion is defined as the impact in the spatial domain caused by modifying DCT coefficients. Different from previous works, here we select coefficients with values ±1, ±2 as cover, which will not cause extra bitrate-expansion and decrease the shift distortion. By minimizing both the modification distortion and shift distortion, a heuristic block selecting strategy is proposed. With the selected coefficients and the corresponding distortion, we use recursive histogram modification under the inconsistent-distortion metric for message embedding. The experimental results show that the proposed method can effectively improve visual quality as well as bring small bitstream expansion. Additionally, the undetectability of the proposed method outperforms those of the existing methods.

The Effect of Sintering Temperature on the Electrical Properties and Particle Size of the Compound Ferroelectric PZT Prepared by Wet Chemical Methods

Lead Zirconate Titanate (PZT) nanopowder of ratio 35/65 (Pb(Zr0.35Ti0.65)O3 is prepared by one of the most wet-chemical routes called Sol-Gel Processing Method. The Lead Zirconate Titanate (PZT) is prepared from Lead Acetate and Zirconate (IV) isopropoxide as a source of metals. The acetic acid can be used as a solvent, and 2-methoxy was used as a stabilizer for Titanate (IV) isoproxide. The heat-treated powders at different sintering temperatures are characterized using the XRD diffraction technique, SEM, and LCR meter. XRD pattern shows the tetragonal phase of 35/65 Zr/Ti composition. They exhibited high density which is slightly different from the theoretical density, decrease of voids, stoichiometric chemical material, and homogeneity from both physical and chemical material. It has been found that each ceramic sample was exhibited different particles size depending on sintering temperature. The present work is well-crystallized with nanoparticles and single-phase perovskite PZT powders that can be obtained after heat treatment above 550°C for two hours. The dependence of this crystallization temperature is observed on the preparation condition. Lattice constant distortion is realized on dielectric constant, especially on the tetragonal phase.

Molecular Parameters of Tert-Butyl Chloride and Its Isotopologues Determined from High-Resolution Rotational Spectroscopy

A broadband chirped-pulse Fourier transform microwave spectrometer was used to detect the rotational spectra of the products of a chemical reaction in the gas phase from 1-18 GHz under the supersonic expansion condition. In natural abundance, pure rotational energy level transitions of tert-butyl chloride and its isotopologues (13C, 37Cl) were observed and assigned. The rotational spectral parameters (rotational constant, quadrupole coupling constant and centrifugal distortion constant) of these isotopologues were determined. The experimental results are in great agreement with the calculated values of quantum chemistry and the spectral parameters in the literature. The accuracy and the capability for chemical detection of our homemade rotational spectrometer were verified by this experiment.

Communication, Distortion, and Randomness in Metric Voting

In distortion-based analysis of social choice rules over metric spaces, voters and candidates are jointly embedded in a metric space. Voters rank candidates by non-decreasing distance. The mechanism, receiving only this ordinal (comparison) information, must select a candidate approximately minimizing the sum of distances from all voters to the chosen candidate. It is known that while the Copeland rule and related rules guarantee distortion at most 5, the distortion of many other standard voting rules, such as Plurality, Veto, or k-approval, grows unboundedly in the number n of candidates.An advantage of Plurality, Veto, or k-approval with small k is that they require less communication from the voters; all deterministic social choice rules known to achieve constant distortion require voters to transmit their complete rankings of all candidates. This motivates our study of the tradeoff between the distortion and the amount of communication in deterministic social choice rules.We show that any one-round deterministic voting mechanism in which each voter communicates only the candidates she ranks in a given set of k positions must have distortion at least 2n-k/k; we give a mechanism achieving an upper bound of O(n/k), which matches the lower bound up to a constant. For more general communication-bounded voting mechanisms, in which each voter communicates b bits of information about her ranking, we show a slightly weaker lower bound of Ω(n/b) on the distortion.For randomized mechanisms, Random Dictatorship achieves expected distortion strictly smaller than 3, almost matching a lower bound of 3 − 2/n for any randomized mechanism that only receives each voter's top choice. We close this gap, by giving a simple randomized social choice rule which only uses each voter's first choice, and achieves expected distortion 3 − 2/n.

Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice

We study social choice mechanisms in an implicit utilitarian framework with a metric constraint, where the goal is to minimize Distortion, the worst case social cost of an ordinal mechanism relative to underlying cardinal utilities. We consider two additional desiderata: Constant sample complexity and Squared Distortion. Constant sample complexity means that the mechanism (potentially randomized) only uses a constant number of ordinal queries regardless of the number of voters and alternatives. Squared Distortion is a measure of variance of the Distortion of a randomized mechanism.Our primary contribution is the first social choice mechanism with constant sample complexity and constant Squared Distortion (which also implies constant Distortion). We call the mechanism Random Referee, because it uses a random agent to compare two alternatives that are the favorites of two other random agents. We prove that the use of a comparison query is necessary: no mechanism that only elicits the top-k preferred alternatives of voters (for constant k) can have Squared Distortion that is sublinear in the number of alternatives. We also prove that unlike any top-k only mechanism, the Distortion of Random Referee meaningfully improves on benign metric spaces, using the Euclidean plane as a canonical example. Finally, among top-1 only mechanisms, we introduce Random Oligarchy. The mechanism asks just 3 queries and is essentially optimal among the class of such mechanisms with respect to Distortion.In summary, we demonstrate the surprising power of constant sample complexity mechanisms generally, and just three random voters in particular, to provide some of the best known results in the implicit utilitarian framework.

Performance management, gaming and monitoring in Israeli organisations

ABSTRACT Recent comparative measures rank Israel very high on the innovation scale and note its preference for informal managerial practices. Based on a principal–agent analysis, this article explains that the economic and administrative systems in Israel have created the basis for the evolution of a managerial culture characterised by constant distortions and the gaming of performance information, lack of truthful reporting and improvisation. On the positive side, this managerial culture encourages innovation; on the negative side, it creates significant problems related to accountability, ethical conduct and overall managerial quality.

Microstructure and optical properties of ZnO nanorods prepared by anodic arc plasma method.

A one-dimensional ZnO nanostructure is a versatile and multifunctional n-type semiconductor. In this paper, ZnO nanorods were successfully prepared by the anodic arc plasma method in an oxidizing atmosphere. The composition, morphology, crystal microstructure, and optical properties of ZnO nanorods were characterized by using X-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM) and the corresponding selected-area electron diffraction (SAED), X-ray energy dispersive spectrometry (XEDS), ultraviolet-visible (UV-VIS) spectroscopy, Raman scattering spectrum (Raman), and photoluminescence spectrum (PL). The experiment results show that ZnO nanorods synthesized by this method possess hexagonal wurtzite crystal structure with good crystallization, no other impurity phases are observed, the crystalline size is about 18 nm, and the lattice constant distortion occurs compared to that of bulk ZnO. The morphology of the sample is a rod-like shape, the length ranges from 100 nm to 300 nm, the average diameter is approximately 20 nm, and the aspect ratio is relatively high. The UV-VIS absorption spectrum occurs red shift, The Raman spectrum further demonstrates that the major peaks are assigned to ZnO optical vibrational modes, and the PL spectrum exhibits coexistence properties of ultraviolet (UV) and green emission. The results prove that ZnO nanorods with hexagonal wurtzite crystal structure were successfully prepared by the anodic arc plasma method in an oxidizing atmosphere.

Modelling and calibration of depth-dependent distortion for large depth visual measurement cameras

Lens distortion parameters vary with the distance between the object point and the image plane. We propose an analytical model of depth-dependent distortion for large depth-of-field digital cameras used for high accuracy photogrammetry. Compared with the magnification-dependent model, the proposed one does not need focusing operation during calibration, thus eliminates focusing errors and guarantees the stability of camera interior parameters. Compared with the widely used constant distortion parameter model, the proposed model reduces the maximum distortion variation from 8.0 μm to 0.9 μm at 20 mm radial distance when the depth changes from 2.46 m to 4.51 m for the 35 mm lens, and from 23.0 μm to 3.6 μm when the depth changes from 2.07 m to 4.17 m for the 50 mm lens. Additionally, when applied to photogrammetry bundle adjustment, the proposed model reduces length measurement standard deviation from 0.055 mm to 0.028 mm in a measurement volume of 7.0 m × 3.5 m × 2.5m compared with the constant parameter model.

Constant Distortion Embeddings of Symmetric Diversities

Abstract Diversities are like metric spaces, except that every finite subset, instead of just every pair of points, is assigned a value. Just as there is a theory of minimal distortion embeddings of fiite metric spaces into L1, there is a similar, yet undeveloped, theory for embedding finite diversities into the diversity analogue of L1 spaces. In the metric case, it iswell known that an n-point metric space can be embedded into L1 withO(log n) distortion. For diversities, the optimal distortion is unknown. Here, we establish the surprising result that symmetric diversities, those in which the diversity (value) assigned to a set depends only on its cardinality, can be embedded in L1 with constant distortion.

The 4-Dimensional Plant: Effects of Wind-Induced Canopy Movement on Light Fluctuations and Photosynthesis.

Physical perturbation of a plant canopy brought about by wind is a ubiquitous phenomenon and yet its biological importance has often been overlooked. This is partly due to the complexity of the issue at hand: wind-induced movement (or mechanical excitation) is a stochastic process which is difficult to measure and quantify; plant motion is dependent upon canopy architectural features which, until recently, were difficult to accurately represent and model in 3-dimensions; light patterning throughout a canopy is difficult to compute at high-resolutions, especially when confounded by other environmental variables. Recent studies have reinforced the expectation that canopy architecture is a strong determinant of productivity and yield; however, links between the architectural properties of the plant and its mechanical properties, particularly its response to wind, are relatively unknown. As a result, biologically relevant data relating canopy architecture, light- dynamics, and short-scale photosynthetic responses in the canopy setting are scarce. Here, we hypothesize that wind-induced movement will have large consequences for the photosynthetic productivity of our crops due to its influence on light patterning. To address this issue, in this study we combined high resolution 3D reconstructions of a plant canopy with a simple representation of canopy perturbation as a result of wind using solid body rotation in order to explore the potential effects on light patterning, interception, and photosynthetic productivity. We looked at two different scenarios: firstly a constant distortion where a rice canopy was subject to a permanent distortion throughout the whole day; and secondly, a dynamic distortion, where the canopy was distorted in incremental steps between two extremes at set time points in the day. We find that mechanical canopy excitation substantially alters light dynamics; light distribution and modeled canopy carbon gain. We then discuss methods required for accurate modeling of mechanical canopy excitation (here coined the 4-dimensional plant) and some associated biological and applied implications of such techniques. We hypothesize that biomechanical plant properties are a specific adaptation to achieve wind-induced photosynthetic enhancement and we outline how traits facilitating canopy excitation could be used as a route for improving crop yield.

Обеспечение электромеханической совместимости в частотно-регулируемых асинхронных электроприводах при регулировании частоты ШИМ

Provision of electromechanical compatibility of asynchronous drive is considered. A computer drive model has been developed to investigate electromechanical processes in systems with PWM-inventors and asynchronous motors. Model calculations show that continuous change in the reference voltage frequency enables a multiple decrease of the amplitude of higher harmonics and electromagnetic torque with constant distortion factor. Vibrations of the electric drive may be decreased due to the reduced amplitudes of the torque harmonics. Motor losses change insignificantly. Variation of the reference voltage frequency within the given range should not to be implemented with frequency of motor supply currents.

A Nonlinear Approach to Dimension Reduction

The $l_2$ flattening lemma of Johnson and Lindenstrauss [JL84] is a powerful tool for dimension reduction. It has been conjectured that the target dimension bounds can be refined and bounded in terms of the intrinsic dimensionality of the data set (for example, the doubling dimension). One such problem was proposed by Lang and Plaut [LP01] (see also [GKL03,MatousekProblems07,ABN08,CGT10]), and is still open. We prove another result in this line of work: The snowflake metric $d^{1/2}$ of a doubling set $S \subset l_2$ embeds with constant distortion into $l_2^D$, for dimension $D$ that depends solely on the doubling constant of the metric. In fact, the distortion can be made arbitrarily close to 1, and the target dimension is polylogarithmic in the doubling constant. Our techniques are robust and extend to the more difficult spaces $l_1$ and $l_\infty$, although the dimension bounds here are quantitatively inferior than those for $l_2$.

The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative-Type Metrics into ℓ 1

In this article, we disprove a conjecture of Goemans and Linial; namely, that every negative type metric embeds into ℓ 1 with constant distortion. We show that for an arbitrarily small constant δ > 0, for all large enough n , there is an n -point negative type metric which requires distortion at least (log log n ) 1/6-δ to embed into ℓ 1 . Surprisingly, our construction is inspired by the Unique Games Conjecture (UGC), establishing a previously unsuspected connection between probabilistically checkable proof systems (PCPs) and the theory of metric embeddings. We first prove that the UGC implies a super-constant hardness result for the (nonuniform) S PARSEST C UT problem. Though this hardness result relies on the UGC, we demonstrate, nevertheless, that the corresponding PCP reduction can be used to construct an “integrality gap instance” for S PARSEST C UT . Towards this, we first construct an integrality gap instance for a natural SDP relaxation of U NIQUE G AMES . Then we “simulate” the PCP reduction and “translate” the integrality gap instance of U NIQUE G AMES to an integrality gap instance of S PARSEST C UT . This enables us to prove a (log log n ) 1/6-δ integrality gap for S PARSEST C UT , which is known to be equivalent to the metric embedding lower bound.

L'oggetto sguardo nell'insegnamento di Lacan

The eye occupies a central place in the teaching of Jacques Lacan. In particular, it finds its almost final formulation in Seminar X (1962-63) and Seminar XI (1964). In these Seminars the field of vision is no longer the place of illusion and mirage of the subjective identity, but it becomes the same field crossed by Freud’s Unheimlich , namely that of the sudden apparition of what is invisible. ‘Look’ is the name that Lacan gives to this appearance. The effects of what Lacan calls the ‘look function’ are: a radical alteration of the coordinates of the visual field and an effect of anguish. In such a perspective, the visual field becomes the proper place to radicalize the idea of the ‘subversion of the subject’: the subject doesn’t look, he/she is looked, the gaze looks at the subject, grabs him/her, and, in doing so, it determines the subject. Thus, Lacan reduces the subject to a claim, a need, that crosses and distorts the visual field. This distortion forces the subject to meet his/her condition of object. From this point of view, visual arts are a privileged territory to establish a certain relationship with the constant distortion of the eye (since aesthetics is, after all, ethics), therefore with that objectual condition that each subject embodies.