Trace Metrics Research Articles

Embedding automated function performance benchmarking, profiling and resource usage categorization in function as a service DevOps pipelines

Function as a Service has enabled a modular development, automated elasticity and cloud-native implementation of applications. The break down into functions can lead to a more fine grained performance profiling of application parts. Embedding this process into the function development lifecycle can give significant benefits such as information per development version, optimized function sizing as well as enhanced function annotation with relation to its resource usage needs, exploited by FaaS providers for optimally co-allocating function executions in an effort to minimize overheads from their concurrent execution. In this paper, a function performance pipeline is created in order to directly analyze the performance of developed functions. The pipeline applies function benchmarking through load generation, profiling of resource usage of that function and categorization of the function relatively to other previous functions run in the framework. A two-step load generation is applied for enhanced validity of trace collection. Information is collected from both the function-side performance view (FaaS platform wait time, initialization and execution duration) as well as the underlying container platform (function level execution traces for CPU, memory, filesystem and network usage). The categorization stage clusters available function trace metrics based on the acquired resource profiles and extracts low/medium/high centroids for each resource metric. These are then used to classify and annotate each new function at the relevant level of activity per resource metric. We have applied the function benchmarking and categorization on 4 example functions (fibonacci, list, sort, and fileRW ones), while testing the effect of the two-stage load generation. The latter portrays an improvement on the profiling acquisition ranging from 1.23x to 45x times across the collected resource metrics. Different function inputs are also applied in order to observe their outcome on the categorization process itself. Finally, 8 different function co-allocation scenarios are applied based on different function categories that indicate concurrency overheads ranging from 15 % to 552 % performance degradation depending on the type of category selected for co-placement.

Information geometry for phylogenetic trees

We propose a new space of phylogenetic trees which we call wald space. The motivation is to develop a space suitable for statistical analysis of phylogenies, but with a geometry based on more biologically principled assumptions than existing spaces: in wald space, trees are close if they induce similar distributions on genetic sequence data. As a point set, wald space contains the previously developed Billera–Holmes–Vogtmann (BHV) tree space; it also contains disconnected forests, like the edge-product (EP) space but without certain singularities of the EP space. We investigate two related geometries on wald space. The first is the geometry of the Fisher information metric of character distributions induced by the two-state symmetric Markov substitution process on each tree. Infinitesimally, the metric is proportional to the Kullback–Leibler divergence, or equivalently, as we show, to any f-divergence. The second geometry is obtained analogously but using a related continuous-valued Gaussian process on each tree, and it can be viewed as the trace metric of the affine-invariant metric for covariance matrices. We derive a gradient descent algorithm to project from the ambient space of covariance matrices to wald space. For both geometries we derive computational methods to compute geodesics in polynomial time and show numerically that the two information geometries (discrete and continuous) are very similar. In particular, geodesics are approximated extrinsically. Comparison with the BHV geometry shows that our canonical and biologically motivated space is substantially different.

Elliptic isometries of the manifold of positive definite real matrices with the trace metric

We study the differential-geometric properties of the loci of fixed points of the elliptic isometries of the manifold of positive definite real matrices with the trace metric. We also give an explicit description of such loci and in particular we find their De Rham decomposition.

HNType : a diverse trace and migration mechanism in the block based Hierarchical Storage System named HazelNut

HazelNut is a block based Hierarchical Storage System, in which logical data blocks are migrated among storage tiers to achieve better I/O performance. In order to choose migrated blocks, data block I/O process is traced to collect enough information for migration algorithms. There are many ways to trace I/O process and implement block migration. However, how to choose trace metrics and design block migration algorithm is a big problem for system designers. To address this problem, a diverse trace and migration mechanism HNType is proposed. HNType consists two parts, one is a diverse trace mechanism named HNType-t, and the other is a diverse migration mechanism named HNType-s. HNType-t abstracts four base elements and trace operation interfaces based on VFS design concept, which makes it feasible to customize specific trace metrics and trace operations; HNType-s presents three ways of data migration, each way of migration can use customized migration algorithms according to predefined prototypes. Based on HNType, A series of tests are conducted about how block migration is affected by different trace metrics, and three conclusions are drawn according to the experiment results. First, trace metrics of access times and access sectors are not linearly correlated, as a result, these two metrics bring different migration result; Second, I/O completion time used as trace metrics is able to improve sequential I/O by at least 10%; Third, access times used as metrics have a tendency of more migrations upwards.

Comparative Study of Trace Metrics between Bibliometrics and Patentometrics

Abstract Purpose To comprehensively evaluate the overall performance of a group or an individual in both bibliometrics and patentometrics. Design/methodology/approach Trace metrics were applied to the top 30 universities in the 2014 Academic Ranking of World Universities (ARWU)—computer sciences, the top 30 ESI highly cited papers in the computer sciences field in 2014, as well as the top 30 assignees and the top 30 most cited patents in the National Bureau of Economic Research (NBER) computer hardware and software category. Findings We found that, by applying trace metrics, the research or marketing impact efficiency, at both group and individual levels, was clearly observed. Furthermore, trace metrics were more sensitive to the different publication-citation distributions than the average citation and h-index were. Research limitations Trace metrics considered publications with zero citations as negative contributions. One should clarify how he/she evaluates a zero-citation paper or patent before applying trace metrics. Practical implications Decision makers could regularly examine the performance of their university/company by applying trace metrics and adjust their policies accordingly. Originality/value Trace metrics could be applied both in bibliometrics and patentometrics and provide a comprehensive view. Moreover, the high sensitivity and unique impact efficiency view provided by trace metrics can facilitate decision makers in examining and adjusting their policies.

Logical Characterization of Trace Metrics

In this paper we continue our research line on logical characterizations of behavioral metrics obtained from the definition of a metric over the set of logical properties of interest. This time we provide a characterization of both strong and weak trace metric on nondeterministic probabilistic processes, based on a minimal boolean logic L which we prove to be powerful enough to characterize strong and weak probabilistic trace equivalence. Moreover, we also prove that our characterization approach can be restated in terms of a more classic probabilistic L-model checking problem.

Distinguishability of quantum states and shannon complexity in quantum cryptography

The proof of the security of quantum key distribution is a rather complex problem. Security is defined in terms different from the requirements imposed on keys in classical cryptography. In quantum cryptography, the security of keys is expressed in terms of the closeness of the quantum state of an eavesdropper after key distribution to an ideal quantum state that is uncorrelated to the key of legitimate users. A metric of closeness between two quantum states is given by the trace metric. In classical cryptography, the security of keys is understood in terms of, say, the complexity of key search in the presence of side information. In quantum cryptography, side information for the eavesdropper is given by the whole volume of information on keys obtained from both quantum and classical channels. The fact that the mathematical apparatuses used in the proof of key security in classical and quantum cryptography are essentially different leads to misunderstanding and emotional discussions [1]. Therefore, one should be able to answer the question of how different cryptographic robustness criteria are related to each other. In the present study, it is shown that there is a direct relationship between the security criterion in quantum cryptography, which is based on the trace distance determining the distinguishability of quantum states, and the criterion in classical cryptography, which uses guesswork on the determination of a key in the presence of side information.

Log-majorization and Lie–Trotter formula for the Cartan barycenter on probability measure spaces

We extend Ando–Hiai's log-majorization for the weighted geometric mean of positive definite matrices into that for the Cartan barycenter in the general setting of probability measures on the Riemannian manifold of positive definite matrices equipped with trace metric. The main key is the settlement of the monotonicity problem of the Cartan barycenteric map on the space of probability measures with finite first moment for the stochastic order induced by the cone. We also derive a version of Lie–Trotter formula and related unitarily invariant norm inequalities for the Cartan barycenter as the main application of log-majorization.

Measuring technological performance of assignees using trace metrics in three fields

The study establishes three synthetic indicators derived from academic traces--assignee traces T1, T2 and ST--and investigates their application in evaluating technological performance of assignees. Patent data for the top 100 assignees in three fields, "Computer Hardware & Software", "Motors, Engines & Parts", and "Drugs & Medical", were retrieved from USPTO for further analysis. The results reveal that traces are indeed valid and useful indicators for measuring technological performance and providing detailed technical information about assignees and the industry. In addition, we investigate the relationship between traces and three other indicators: patent citation counts, Current Impact Index and patent h-index. In comparison with the three other indicators, traces demonstrate unique advantages and can be a good complement to patent citation analysis.

The power mean and the least squares mean of probability measures on the space of positive definite matrices

In this paper we derive properties of the least squares (or Karcher) mean of probability measures on the open cone Ω of positive definite matrices of some fixed dimension endowed with the trace metric that generalize known properties of the weighted least squares mean of finitely many positive definite matrices. Our approach is based on first defining the t-power mean of a probability measure as the unique fixed point of the contractive mapX∈Ω↦∫ΩX#tZμ(dZ) with respect to the Thompson metric, establishing its properties analogous to those of the power mean for a finite number of positive definite matrices, and showing the t-power means converge to the Karcher mean as t→0. We carry out this program first of all for the compactly supported probability measures and show that theory including the monotonicity extends to the general case.

The least squares mean of positive Hilbert–Schmidt operators

We show that, the least squares mean on the Riemannian manifold Σ of positive operators in the extended Hilbert–Schmidt algebra of linear operators on a Hilbert space equipped with the canonical trace metric is the unique solution of the corresponding Karcher equation. This allows us to conclude that, the least squares mean is the restriction of the Karcher mean on the open cone of all bounded positive definite operators, and hence inherits the basic properties of that mean. Conversely, the Karcher mean on the positive definite operators is shown to be the unique monotonically strongly continuous extension of the least squares mean on Σ.

Matrix power means and the Karcher mean

We define a new family of matrix means { P t ( ω ; A ) } t ∈ [ − 1 , 1 ] , where ω and A vary over all positive probability vectors in R n and n-tuples of positive definite matrices resp. Each of these means except t ≠ 0 arises as a unique positive definite solution of a non-linear matrix equation, satisfies all desirable properties of power means of positive real numbers and interpolates between the weighted harmonic and arithmetic means. The main result is that the Karcher mean coincides with the limit of power means as t → 0 . This provides not only a sequence of matrix means converging to the Karcher mean, but also a simple proof of the monotonicity of the Karcher mean, conjectured by Bhatia and Holbrook, and other new properties, which have recently been established by Lawson and Lim and also Bhatia and Karandikar using probabilistic methods on the metric structure of positive definite matrices equipped with the trace metric.

Chameleon

Languages such as Java and C#, as well as scripting languages like Python, and Ruby, make extensive use of Collection classes. A collection implementation represents a fixed choice in the dimensions of operation time, space utilization, and synchronization. Using the collection in a manner not consistent with this fixed choice can cause significant performance degradation. In this paper, we present CHAMELEON, a low-overhead automatic tool that assists the programmer in choosing the appropriate collection implementation for her application. During program execution, CHAMELEON computes elaborate trace and heap-based metrics on collection behavior. These metrics are consumed on-thefly by a rules engine which outputs a list of suggested collection adaptation strategies. The tool can apply these corrective strategies automatically or present them to the programmer. We have implemented CHAMELEON on top of a IBM's J9 production JVM, and evaluated it over a small set of benchmarks. We show that for some applications, using CHAMELEON leads to a significant improvement of the memory footprint of the application.

The Monge metric on the sphere and geometry of quantum states

Topological and geometrical properties of the set of mixed quantum states in the N-dimensional Hilbert space are analysed. Assuming that the corresponding classical dynamics takes place on the sphere we use the vector SU(2) coherent states and the generalised Husimi distributions to define the Monge distance between arbitrary two density matrices. The Monge metric has a simple semiclassical interpretation and induces a non-trivial geometry. Among all pure states the distance from the maximally mixed state \rho_*, proportional to the identity matrix, admits the largest value for the coherent states, while the delocalized 'chaotic' states are close to \rho_*. This contrasts the geometries induced by the standard (trace, Hilbert-Schmidt or Bures) metrics, where the distance from \rho_* is the same for all pure states. We discuss possible physical consequences including unitary time evolution and the process of decoherence. We introduce also a simplified Monge metric, defined in the space of pure quantum states, and more suitable for numerical computation.

Tensor operators and the trace metric

The traditional unit tensor operators are shown to be orthonormal vectors in a trace metric approach. The operator equivalents of crystal field theory are used as models of the tensor operators which act as generators in Lie group theory.