General-purpose Method Research Articles

Continued Fractions Applied to the One Line Factoring Algorithm for Breaking RSA

The RSA (Rivest–Shamir–Adleman) cryptosystem is an asymmetric public key cryptosystem popular for its use in encryptions and digital signatures. However, the Wiener’s attack on the RSA cryptosystem utilizes continued fractions, which has generated much interest in developing competitive factoring algorithms. A general-purpose integer factorization method first proposed by Lehmer and Powers formed the basis of the well-known Continued Fraction Factorization (CFRAC) method. Recent work on the one line factoring algorithm by Hart and its connection with Lehman’s factoring method have motivated this paper. The emphasis of this paper is to explore the representations of PQ as continued fractions and the suitability of lower ordered convergences as representations of ab. These simpler convergences are then prescribed to Hart’s one line factoring algorithm. As an illustration, we demonstrate the working of our approach with two numbers: one smaller number and another larger number occupying 95 bits. Using our method, the fourth convergence finds the factors as the solution for the smaller number, while the eleventh convergence finds the factors for the larger number. The security of the RSA public key cryptosystem relies on the computational difficulty of factoring large integers. Among the challenges in breaking RSA semi-primes, RSA250, which is an 829-bit semi-prime, continues to hold a research record. In this paper, we apply our method to factorize RSA250 and present the practical implementation of our algorithm. Our approach’s theoretical and experimental findings demonstrate the reduction of the search space and a faster solution to the semi-prime factorization problem, resulting in key contributions and practical implications. We identify further research to extend our approach by exploring limitations and additional considerations such as the difference of squares method, paving the way for further research in this direction.

CIDER: Context-sensitive polarity measurement for short-form text.

Researchers commonly perform sentiment analysis on large collections of short texts like tweets, Reddit posts or newspaper headlines that are all focused on a specific topic, theme or event. Usually, general-purpose sentiment analysis methods are used. These perform well on average but miss the variation in meaning that happens across different contexts, for example, the word "active" has a very different intention and valence in the phrase "active lifestyle" versus "active volcano". This work presents a new approach, CIDER (Context Informed Dictionary and sEmantic Reasoner), which performs context-sensitive linguistic analysis, where the valence of sentiment-laden terms is inferred from the whole corpus before being used to score the individual texts. In this paper, we detail the CIDER algorithm and demonstrate that it outperforms state-of-the-art generalist unsupervised sentiment analysis techniques on a large collection of tweets about the weather. CIDER is also applicable to alternative (non-sentiment) linguistic scales. A case study on gender in the UK is presented, with the identification of highly gendered and sentiment-laden days. We have made our implementation of CIDER available as a Python package: https://pypi.org/project/ciderpolarity/.

СПЕЦІАЛІЗОВАНЕ ПОПЕРЕДНЄ НАВЧАННЯ НЕЙРОМЕРЕЖЕВИХ МОДЕЛЕЙ НА СИНТЕТИЧНИХ ДАНИХ ДЛЯ ПОКРАЩЕННЯ ГЕНЕРАЦІЇ ПЕРЕФРАЗУВАННЯ

SPECIALIZED PRE-TRAINING OF NEURAL NETWORKS ON SYNTHETIC DATA FOR IMPROVING PARAPHRASE GENERATION Abstract. Generating paraphrases is a fundamental problem in natural language processing. In light of the significant success of transfer learning technology, the “pre-training fine-tuning” approach has become the standard. However, popular general-purpose pre-training methods typically require large datasets and computational resources, and available pre-trained models are limited by fixed architecture and size. We propose a simple and effective approach for pre-training specifically for paraphrase generation, which significantly improves model quality and matches the quality level of general-purpose models. Both existing public data and new data generated by large language models were used. The impact of this procedure on neural networks of different architectures was investigated, and it was shown to work for all of them. Keywords: artificial intelligence, machine learning, neural networks, paraphrase generation, pre-training, fine-tuning.

An Advance Study of an Efficient CNN-Grounded Deep Learning Classification Technique for the Diagnosis of IoT based Cardiac Arrhythmias

Deep Learning, or DL for short, is an emerging subfield within the larger discipline of machine learning in today's world. The study being conducted in this area is progressing at an immediate stride, and the discoveries are contributing to the progression of technology. Deep learning (DL) methods were developed with the intention of developing a general-purpose learning method that would enable the gradual learning of characteristics at multiple levels without relying on human-engineered features. This was the goal of deep learning. Because of this, the system is able to acquire intricate purposes and directly map input to output by making use of the data that it has acquired which is based on Internet of things (IoTs). This study places an emphasis on the application of CNN (Convolutional Neural Networks), which are a subcategory of DNN (Deep Neural Networks), and it develops an efficient layered CNN for the classification of ECG arrhythmias. Even while FC-ANNs (Fully Connected Artificial Neural Networks), which are sometimes referred to as Multilayer-Perceptron networks, are effective in categorising ECG arrhythmias, the optimization process for many classification networks takes a significant amount of time in terms of computation. In addition, the features extracted by engineers are what define the accuracy of the categorization of ECG arrhythmias. An improved CNN based filtering, feature abstraction, and classification prototypical is established in order to conduct an accurate analysis of an electrocardiogram (ECG). When measured against ANN, the performance was found to have an accuracy rating of 99.6%. Consequently, the CNN model that was suggested is useful to doctors in arriving at the definitive diagnosis of AFL (atrial flutter), AFIB (atrial fibrillation), VFL (ventricular flutter), and VT (ventricular tachycardia). It includes denoising, feature extraction, and categorization as part of its functionality.

Segmentation of Dynamic Total-Body [18F]-FDG PET Images Using Unsupervised Clustering.

Clustering time activity curves of PET images have been used to separate clinically relevant areas of the brain or tumours. However, PET image segmentation in multiorgan level is much less studied due to the available total-body data being limited to animal studies. Now, the new PET scanners providing the opportunity to acquire total-body PET scans also from humans are becoming more common, which opens plenty of new clinically interesting opportunities. Therefore, organ-level segmentation of PET images has important applications, yet it lacks sufficient research. In this proof of concept study, we evaluate if the previously used segmentation approaches are suitable for segmenting dynamic human total-body PET images in organ level. Our focus is on general-purpose unsupervised methods that are independent of external data and can be used for all tracers, organisms, and health conditions. Additional anatomical image modalities, such as CT or MRI, are not used, but the segmentation is done purely based on the dynamic PET images. The tested methods are commonly used building blocks of the more sophisticated methods rather than final methods as such, and our goal is to evaluate if these basic tools are suited for the arising human total-body PET image segmentation. First, we excluded methods that were computationally too demanding for the large datasets from human total-body PET scanners. These criteria filtered out most of the commonly used approaches, leaving only two clustering methods, k-means and Gaussian mixture model (GMM), for further analyses. We combined k-means with two different preprocessing approaches, namely, principal component analysis (PCA) and independent component analysis (ICA). Then, we selected a suitable number of clusters using 10 images. Finally, we tested how well the usable approaches segment the remaining PET images in organ level, highlight the best approaches together with their limitations, and discuss how further research could tackle the observed shortcomings. In this study, we utilised 40 total-body [18F] fluorodeoxyglucose PET images of rats to mimic the coming large human PET images and a few actual human total-body images to ensure that our conclusions from the rat data generalise to the human data. Our results show that ICA combined with k-means has weaker performance than the other two computationally usable approaches and that certain organs are easier to segment than others. While GMM performed sufficiently, it was by far the slowest one among the tested approaches, making k-means combined with PCA the most promising candidate for further development. However, even with the best methods, the mean Jaccard index was slightly below 0.5 for the easiest tested organ and below 0.2 for the most challenging organ. Thus, we conclude that there is a lack of accurate and computationally light general-purpose segmentation method that can analyse dynamic total-body PET images.

KMD clustering: robust general-purpose clustering of biological data

The noisy and high-dimensional nature of biological data has spawned advanced clustering algorithms that are tailored for specific biological datatypes. However, the performance of such methods varies greatly between datasets and they require post hoc tuning of cryptic hyperparameters. We present k minimal distance (KMD) clustering, a general-purpose method based on a generalization of single and average linkage hierarchical clustering. We introduce a generalized silhouette-like function to eliminate the cryptic hyperparameter k, and use sampling to enable application to million-object datasets. Rigorous comparisons to general and specialized clustering methods on simulated, mass cytometry and scRNA-seq datasets show consistent high performance of KMD clustering across all datasets.

Introducing instance label correlation in multiple instance learning. Application to cancer detection on histopathological images

In the last years, the weakly supervised paradigm of multiple instance learning (MIL) has become very popular in many different areas. A paradigmatic example is computational pathology, where the lack of patch-level labels for whole-slide images prevents the application of supervised models. Probabilistic MIL methods based on Gaussian Processes (GPs) have obtained promising results due to their excellent uncertainty estimation capabilities. However, these are general-purpose MIL methods that do not take into account one important fact: in (histopathological) images, the labels of neighboring patches are expected to be correlated. In this work, we extend a state-of-the-art GP-based MIL method, which is called VGPMIL-PR, to exploit such correlation. To do so, we develop a novel coupling term inspired by the statistical physics Ising model. We use variational inference to estimate all the model parameters. Interestingly, the VGPMIL-PR formulation is recovered when the weight that regulates the strength of the Ising term vanishes. The performance of the proposed method is assessed in two real-world problems of prostate cancer detection. We show that our model achieves better results than other state-of-the-art probabilistic MIL methods. We also provide different visualizations and analysis to gain insights into the influence of the novel Ising term. These insights are expected to facilitate the application of the proposed model to other research areas.

DeepFTSG: Multi-stream Asymmetric USE-Net Trellis Encoders with Shared Decoder Feature Fusion Architecture for Video Motion Segmentation

Discriminating salient moving objects against complex, cluttered backgrounds, with occlusions and challenging environmental conditions like weather and illumination, is essential for stateful scene perception in autonomous systems. We propose a novel deep architecture, named DeepFTSG, for robust moving object detection that incorporates single and multi-stream multi-channel USE-Net trellis asymmetric encoders extending U-Net with squeeze and excitation (SE) blocks and a single shared decoder network for fusing multiple motion and appearance cues. DeepFTSG is a deep learning based approach that builds upon our previous hand-engineered flux tensor split Gaussian (FTSG) change detection video analysis algorithm which won the CDNet CVPR Change Detection Workshop challenge competition. DeepFTSG generalizes much better than top-performing motion detection deep networks, such as the scene-dependent ensemble-based FgSegNet_v2, while using an order of magnitude fewer weights. Short-term motion and longer-term change cues are estimated using general-purpose unsupervised methods—flux tensor and multi-modal background subtraction, respectively. DeepFTSG was evaluated using the CDnet-2014 change detection challenge dataset, the largest change detection video sequence benchmark with 12.3 billion labeled pixels, and had an overall F-measure of 97%. We also evaluated the cross-dataset generalization capability of DeepFTSG trained solely on CDnet-2014 short video segments and then evaluated on unseen SBI-2015, LASIESTA and LaSOT benchmark videos. On the unseen SBI-2015 dataset, DeepFTSG had an F-measure accuracy of 87%, more than 30% higher compared to the top-performing deep network FgSegNet_v2 and outperforms the recently proposed KimHa method by 17%. On the unseen LASIESTA, DeepFTSG had an F-measure of 88% and outperformed the best recent deep learning method BSUV-Net2.0 by 3%. On the unseen LaSOT with axis-aligned bounding box ground-truth, network segmentation masks were converted to bounding boxes for evaluation, DeepFTSG had an F-Measure of 55%, outperforming KimHa method by 14% and FgSegNet_v2 by almost 1.5%. When a customized single DeepFTSG model is trained in a scene-dependent manner for comparison with state-of-the-art approaches, then DeepFTSG performs significantly better, reaching an F-Measure of 97% on SBI-2015 (+ 10%) and 99% on LASIESTA (+ 11%). The source code, pre-trained weights, and video demo for DeepFTSG are available at https://github.com/CIVA-Lab/DeepFTSG.

Scikit-matter : A Suite of Generalisable Machine Learning Methods Born out of Chemistry and Materials Science.

Easy-to-use libraries such as scikit-learn have accelerated the adoption and application of machine learning (ML) workflows and data-driven methods. While many of the algorithms implemented in these libraries originated in specific scientific fields, they have gained in popularity in part because of their generalisability across multiple domains. Over the past two decades, researchers in the chemical and materials science community have put forward general-purpose machine learning methods. The deployment of these methods into workflows of other domains, however, is often burdensome due to the entanglement with domainspecific functionalities. We present the python library scikit-matter that targets domain-agnostic implementations of methods developed in the computational chemical and materials science community, following the scikit-learn API and coding guidelines to promote usability and interoperability with existing workflows.

A minimum assumption approach to MEG sensor array design.

Objective.Our objective is to formulate the problem of the magnetoencephalographic (MEG) sensor array design as a well-posed engineering problem of accurately measuring the neuronal magnetic fields. This is in contrast to the traditional approach that formulates the sensor array design problem in terms of neurobiological interpretability the sensor array measurements.Approach.We use the vector spherical harmonics (VSH) formalism to define a figure-of-merit for an MEG sensor array. We start with an observation that, under certain reasonable assumptions, any array ofmperfectly noiseless sensors will attain exactly the same performance, regardless of the sensors' locations and orientations (with the exception of a negligible set of singularly bad sensor configurations). We proceed to the conclusion that under the aforementioned assumptions, the only difference between different array configurations is the effect of (sensor) noise on their performance. We then propose a figure-of-merit that quantifies, with a single number, how much the sensor array in question amplifies the sensor noise.Main results.We derive a formula for intuitively meaningful, yet mathematically rigorous figure-of-merit that summarizes how desirable a particular sensor array design is. We demonstrate that this figure-of-merit is well-behaved enough to be used as a cost function for a general-purpose nonlinear optimization methods such as simulated annealing. We also show that sensor array configurations obtained by such optimizations exhibit properties that are typically expected of 'high-quality' MEG sensor arrays, e.g. high channel information capacity.Significance.Our work paves the way toward designing better MEG sensor arrays by isolating the engineering problem of measuring the neuromagnetic fields out of the bigger problem of studying brain function through neuromagnetic measurements.

Two-dimensional radial integration displacement discontinuity method with high-order isoparametric elements

To improve the accuracy of Displacement Discontinuity Method and enhance its adaptivity, a general-purpose two-dimensional displacement discontinuity method with both linear and quadratic isoparametric elements has been developed to model engineering discontinuity problems where cracks or cavities are involved. Linear and quadratic isoparametric elements have linear and quadratic distributions of displacement discontinuity, respectively. Both of them belong to the discontinuous element type, in which the geometry shape functions are different from the interpolation shape functions. A new general formulation, based on the boundary integral functions, is given for displacement discontinuity problems with arbitrary boundary shapes. This formulation contains singular and strongly singular integrals which can be evaluated in the sense of Cauchy principal value and Hadamard principal value, respectively. The radial integration technique is applied to perform these singular integrals with sufficiently high accuracy. Five numerical examples, most of which have analytic solutions, are given to illustrate the improved accuracy of the proposed approach. Compared with the constant displacement discontinuity element, the numerical results by using the present isoparametric displacement discontinuity elements show better accuracy.

Validation of machine learning ridge regression models using Monte Carlo, bootstrap, and variations in cross-validation

Abstract In recent years, there have been several calls by practitioners of machine learning to provide more guidelines on how to use its methods and techniques. For example, the current literature on resampling methods is confusing and sometimes contradictory; worse, there are sometimes no practical guidelines offered at all. To address this shortcoming, a simulation study was conducted that evaluated ridge regression models fitted on five real-world datasets. The study compared the performance of four resampling methods, namely, Monte Carlo resampling, bootstrap, k-fold cross-validation, and repeated k-fold cross-validation. The goal was to find the best-fitting λ (regularization) parameter that would minimize mean squared error, by using nine variations of these resampling methods. For each of the nine resampling variations, 1,000 runs were performed to see how often a good fit, average fit, and poor fit λ value would be chosen. The resampling method that chose good fit values the greatest number of times was deemed the best method. Based on the results of the investigation, three general recommendations are made: (1) repeated k-fold cross-validation is the best method to select as a general-purpose resampling method; (2) k = 10 folds is a good choice in k-fold cross-validation; (3) Monte Carlo and bootstrap are underperformers, so they are not recommended as general-purpose resampling methods. At the same time, no resampling method was found to be uniformly better than the others.

Fisher markets with linear constraints: Equilibrium properties and efficient distributed algorithms

The Fisher market is one of the most fundamental models for resource allocation. However, Fisher markets are less amenable for resource allocation settings when agents have additional linear constraints beyond the budget constraints of buyers and the capacity constraints of goods. Thus, in this work, we introduce a modified Fisher market, where agents may have additional linear constraints, and study the properties of the resulting equilibria. To set equilibrium prices, we introduce a budget-adjusted social optimization problem (BA-SOP), whose optimal dual variables correspond to the equilibrium prices. Since solving BA-SOP can be computationally intensive and requires centralized knowledge of all agents' utilities, we propose a new class of distributed algorithms based on the Alternating Direction Method of Multipliers (ADMM) to compute equilibrium prices. Our ADMM approach has strong convergence guarantees and provides a general-purpose method for computing market equilibria for Fisher markets with homogeneous linear constraints and classical Fisher markets.

CLUE-AD: A Context-Based Method for Labeling Unobserved Entities in Autonomous Driving Data

Generating high-quality annotations for object detection and recognition is a challenging and important task, especially in relation to safety-critical applications such as autonomous driving (AD). Due to the difficulty of perception in challenging situations such as occlusion, degraded weather, and sensor failure, objects can go unobserved and unlabeled. In this paper, we present CLUE-AD, a general-purpose method for detecting and labeling unobserved entities by leveraging the object continuity assumption within the context of a scene. This method is dataset-agnostic, supporting any existing and future AD datasets. Using a real-world dataset representing complex urban driving scenes, we demonstrate the applicability of CLUE-AD for detecting unobserved entities and augmenting the scene data with new labels.

Fast Semantic Segmentation of Remote Sensing Images Using a Network That Integrates Global and Local Information.

Efficient processing of ultra-high-resolution images is increasingly sought after with the continuous advancement of photography and sensor technology. However, the semantic segmentation of remote sensing images lacks a satisfactory solution to optimize GPU memory utilization and the feature extraction speed. To tackle this challenge, Chen et al. introduced GLNet, a network designed to strike a better balance between GPU memory usage and segmentation accuracy when processing high-resolution images. Building upon GLNet and PFNet, our proposed method, Fast-GLNet, further enhances the feature fusion and segmentation processes. It incorporates the double feature pyramid aggregation (DFPA) module and IFS module for local and global branches, respectively, resulting in superior feature maps and optimized segmentation speed. Extensive experimentation demonstrates that Fast-GLNet achieves faster semantic segmentation while maintaining segmentation quality. Additionally, it effectively optimizes GPU memory utilization. For example, compared to GLNet, Fast-GLNet's mIoU on the Deepglobe dataset increased from 71.6% to 72.1%, and GPU memory usage decreased from 1865 MB to 1639 MB. Notably, Fast-GLNet surpasses existing general-purpose methods, offering a superior trade-off between speed and accuracy in semantic segmentation.

Structure-inducing pre-training

Language model pre-training and the derived general-purpose methods have reshaped machine learning research. However, there remains considerable uncertainty regarding why pre-training improves the performance of downstream tasks. This challenge is pronounced when using language model pre-training in domains outside of natural language. Here we investigate this problem by analysing how pre-training methods impose relational structure in induced per-sample latent spaces—that is, what constraints do pre-training methods impose on the distance or geometry between the pre-trained embeddings of samples. A comprehensive review of pre-training methods reveals that this question remains open, despite theoretical analyses showing the importance of understanding this form of induced structure. Based on this review, we introduce a pre-training framework that enables a granular and comprehensive understanding of how relational structure can be induced. We present a theoretical analysis of the framework from the first principles and establish a connection between the relational inductive bias of pre-training and fine-tuning performance. Empirical studies spanning three data modalities and ten fine-tuning tasks confirm theoretical analyses, inform the design of novel pre-training methods and establish consistent improvements over a compelling suite of methods.

Optimizing Quantum Classification Algorithms on Classical Benchmark Datasets.

The discovery of quantum algorithms offering provable advantages over the best known classical alternatives, together with the parallel ongoing revolution brought about by classical artificial intelligence, motivates a search for applications of quantum information processing methods to machine learning. Among several proposals in this domain, quantum kernel methods have emerged as particularly promising candidates. However, while some rigorous speedups on certain highly specific problems have been formally proven, only empirical proof-of-principle results have been reported so far for real-world datasets. Moreover, no systematic procedure is known, in general, to fine tune and optimize the performances of kernel-based quantum classification algorithms. At the same time, certain limitations such as kernel concentration effects-hindering the trainability of quantum classifiers-have also been recently pointed out. In this work, we propose several general-purpose optimization methods and best practices designed to enhance the practical usefulness of fidelity-based quantum classification algorithms. Specifically, we first describe a data pre-processing strategy that, by preserving the relevant relationships between data points when processed through quantum feature maps, substantially alleviates the effect of kernel concentration on structured datasets. We also introduce a classical post-processing method that, based on standard fidelity measures estimated on a quantum processor, yields non-linear decision boundaries in the feature Hilbert space, thus achieving the quantum counterpart of the radial basis functions technique that is widely employed in classical kernel methods. Finally, we apply the so-called quantum metric learning protocol to engineer and adjust trainable quantum embeddings, demonstrating substantial performance improvements on several paradigmatic real-world classification tasks.

Carrier-envelope offset frequency measurement by means of an external optical resonator

A general-purpose method based on the implementation of the asymmetric Pound–Drever–Hall (PDH) technique is proposed to measure the carrier-envelope offset (CEO) frequency of a mode-locked laser using an external optical cavity. By analyzing the synchronously demodulated signal of the spectrally filtered cavity reflection when the optical resonator is locked to the mode-locked laser, a discriminating signal depending on the relative frequency offset between the mode-locked and optical cavity comb-like spectra is obtained. For a given geometry and group delay dispersion (GDD) of the cavity parameters (i.e., a known cavity mode offset), this signal can be used to retrieve the laser CEO. This approach turns out to be advantageous in terms of setup complexity with respect to other well-known techniques that rely on non-linear frequency generation, such as f–2f interferometers. In addition, this method can be used to precisely determine the laser–cavity spectral coupling, which is an important topic in cavity-enhanced spectroscopy and non-linear optics applications. After the theoretical description of the generalized asymmetric PDH signal, an experimental validation of the proposed method is reported using an Er-doped fiber frequency comb source centered at 1,550 nm, with a repetition rate of 250 MHz, locked to a linear optical cavity with a 1 GHz free spectral range. The theoretical effect of the GDD is confirmed experimentally using different cavity configurations. Moreover, the comparison with the CEO frequency values measured using an f–2f interferometer demonstrates the feasibility of the proposed method.

Scikit-matter : A Suite of Generalisable Machine Learning Methods Born out of Chemistry and Materials Science

Easy-to-use libraries such as scikit-learn have accelerated the adoption and application of machine learning (ML) workflows and data-driven methods. While many of the algorithms implemented in these libraries originated in specific scientific fields, they have gained in popularity in part because of their generalisability across multiple domains. Over the past two decades, researchers in the chemical and materials science community have put forward general-purpose machine learning methods. The deployment of these methods into workflows of other domains, however, is often burdensome due to the entanglement with domain-specific functionalities. We present the python library scikit-matter that targets domain-agnostic implementations of methods developed in the computational chemical and materials science community, following the scikit-learn API and coding guidelines to promote usability and interoperability with existing workflows.

Effective Thermal Conductivity Measurement of Additively Manufactured Lattice Structures by Application of Modified Temperature Profile Method

This study aims to establish a general-purpose thermal conductivity measurement method that can take into account the effect of heat loss under atmospheric conditions for measuring the effective thermal conductivity of lattice structures, and to clarify the effective thermal conductivity of lattice structures with different wire diameters. In this paper, calculations by finite element method and measurements using steady state comparative-longitudinal heat flow method and modified temperature profile method were performed to clarify the effective thermal conductivity of the five truncated octahedron unit-cell lattice structures with different wire diameters fabricated by additive manufacturing. The modified temperature profile method is developed to take into account the effect of interfacial thermal resistance in the measurement apparatus. The effective thermal conductivity measured using the steady state comparative-longitudinal heat flow method and calculated with finite element method analysis showed good agreement, confirming that the effective thermal conductivity is strongly dependent on the wire diameter. The effective thermal conductivity obtained by the modified temperature profile (MTP) method was 3 % to 24 % smaller than that obtained by the steady state comparative-longitudinal heat flow method, and the measurement was able to take heat loss into account more concretely. Furthermore, measurements using the MTP method enabled us to obtain reasonable values for the ratio of heat loss in each section, the fin efficiency of the sample, the heat transfer coefficient to the surroundings, and the interfacial thermal resistance between the rods and the sample.