Search

Aiming to uncover the CP properties of spin-0 particle Dark Matter (DM), we explore a two-component DM scenario within the framework of 3-Higgs Doublet Models (3HDMs), a well-motivated set-up previously studied due to the complementarity of its collider and astrophysical probes. We devise benchmark points in which the two components of DM have same CP in one case and opposite CP in another. We then show several cross section distributions of observables at collider experiments where the two cases are clearly distinguishable., Comment: 27 pages, 10 figures

Compared to electronic phase transitions, structural phase transitions of crystals are challenging to control due to the energy cost of breaking dense solid bonds. Recently, however, electric field switching of stacking configuration between honeycomb layers, held together by relatively weak van der Waals (vdW) attractions, was demonstrated. In response to the external fields, the layers slide between commensurate meta-stable configurations with discrete symmetries and distinct lattice orientations. These 2D vdW polytypes host diverse electronic orders such as ferroelectricity and magnetism, providing multiferroic switching via lubricant sliding of incommensurate boundary strips. Ahead, we address recent observations in honeycomb polytypes and identify remaining challenges for extending this conceptual "SlideTronics" mechanism into rapid, local, and practical multiferroic devices. The stacking energies, symmetries, and orbital overlaps that underlie the band structures and internal charge distributions are discussed, along with poly-properties like interfacial-ferroelectricity, ladder-like cumulative polarization, superconductivity, and orbital magnetic orders. Distinct from conventional 3D multiferroic crystals, the 2D vdW assembly and the sliding switching mechanism open poly-opportunities for novel device concepts.

Over the last four decades, a number of modified gravity theories have been proposed to study cosmological phenomena as they can provide solutions for some of the shortcomings of Einstein's gravity in explaining early and late time accelerations of the observed Universe, the existence of dark matter, singularities at center of Black holes etc. The theoretical and observational challenges faced by the $\Lambda$CDM model also point towards the necessity for looking beyond General Relativity. In this direction, recently $f(\phi, T)$ gravity has been proposed in literature where the non-minimal coupling of the scalar field $\phi$ with the trace of energy-momentum tensor $T$ has been introduced in the Einstein-Hilbert action. Considering the Hilltop potential, we have studied the slow-roll inflation in the framework of $f(\phi, T)$ gravity. It is found that Hilltop inflationary models in $f(\phi, T)$ gravity are viable when seen in the light of latest Planck data.

We study warm inflation in the framework of $f(\phi)T$ gravity, where $\phi$ is the inflaton and $T$ is the trace of the energy-momentum tensor. The inflaton field is assumed to roll on the natural potential and the result is analyzed in light of Planck 2018 and BICEP/Keck 2021 data. We start our work by obtaining the field equations under slow-roll approximations. We then evaluate the scalar and tensor power spectra and their corresponding spectral index and tensor-to-scalar ratio with a temperature-dependent form of the dissipation coefficient during the inflationary era. We find that the warm inflation model in $f(\phi)T$ gravity is compatible with observational bands.

Recurrent large language models that compete with Transformers in language modeling perplexity are emerging at a rapid rate (e.g., Mamba, RWKV). Excitingly, these architectures use a constant amount of memory during inference. However, due to the limited memory, recurrent LMs cannot recall and use all the information in long contexts leading to brittle in-context learning (ICL) quality. A key challenge for efficient LMs is selecting what information to store versus discard. In this work, we observe the order in which information is shown to the LM impacts the selection difficulty. To formalize this, we show that the hardness of information recall reduces to the hardness of a problem called set disjointness (SD), a quintessential problem in communication complexity that requires a streaming algorithm (e.g., recurrent model) to decide whether inputted sets are disjoint. We empirically and theoretically show that the recurrent memory required to solve SD changes with set order, i.e., whether the smaller set appears first in-context. Our analysis suggests, to mitigate the reliance on data order, we can put information in the right order in-context or process prompts non-causally. Towards that end, we propose: (1) JRT-Prompt, where context gets repeated multiple times in the prompt, effectively showing the model all data orders. This gives $11.0 \pm 1.3$ points of improvement, averaged across $16$ recurrent LMs and the $6$ ICL tasks, with $11.9\times$ higher throughput than FlashAttention-2 for generation prefill (length $32$k, batch size $16$, NVidia H100). We then propose (2) JRT-RNN, which uses non-causal prefix-linear-attention to process prompts and provides $99\%$ of Transformer quality at $360$M params., $30$B tokens and $96\%$ at $1.3$B params., $50$B tokens on average across the tasks, with $19.2\times$ higher throughput for prefill than FA2.

We report improved wave function for mesons in QCD potential model approach using multiplicative method for solution of Schr\"{o}dinger equation for the extreme cases of inter-quark separations ($r\rightarrow0$ and $r\rightarrow\infty$). Using the wave function we find the range of the scale factor c of the Cornell potential with reference to the mass scale of B and D sectors heavy-flavoured mesons. With our computed range of c, we also explore the critical inter-quark separation which should govern the choice of parent-child terms in perturbation method out of the linear and Coulombic terms of the Cornell potential.

Multi-wavelength polarimetry and radio observations of Swift J1727.8-1613 at the beginning of its recent 2023 outburst suggested the presence of a bright compact jet aligned in the north-south direction, which could not be confirmed without high angular resolution images. Using the Very Long Baseline Array and the Long Baseline Array, we imaged Swift J1727.8-1613, during the hard/hard-intermediate state, revealing a bright core and a large, two-sided, asymmetrical, resolved jet. The jet extends in the north-south direction, at a position angle of $-0.60\pm0.07\deg$ East of North. At 8.4 GHz, the entire resolved jet structure is $\sim110 (d/2.7\,\text{kpc})/\sin i$ AU long, with the southern approaching jet extending $\sim80 (d/2.7\,\text{kpc})/\sin i$ AU from the core, where $d$ is the distance to the source and $i$ is the inclination of the jet axis to the line of sight. These images reveal the most resolved continuous X-ray binary jet, and possibly the most physically extended continuous X-ray binary jet ever observed. Based on the brightness ratio of the approaching and receding jets, we put a lower limit on the intrinsic jet speed of $\beta\geq0.27$ and an upper limit on the jet inclination of $i\leq74\deg$. In our first observation we also detected a rapidly fading discrete jet knot $66.89\pm0.04$ mas south of the core, with a proper motion of $0.66\pm0.05$ mas hour$^{-1}$, which we interpret as the result of a downstream internal shock or a jet-ISM interaction, as opposed to a transient relativistic jet launched at the beginning of the outburst., Comment: Accepted in ApJL

Deep learning models have achieved remarkable success across diverse domains. However, the intricate nature of these models often impedes a clear understanding of their decision-making processes. This is where Explainable AI (XAI) becomes indispensable, offering intuitive explanations for model decisions. In this work, we propose a simple yet highly effective approach, ScoreCAM++, which introduces modifications to enhance the promising ScoreCAM method for visual explainability. Our proposed approach involves altering the normalization function within the activation layer utilized in ScoreCAM, resulting in significantly improved results compared to previous efforts. Additionally, we apply an activation function to the upsampled activation layers to enhance interpretability. This improvement is achieved by selectively gating lower-priority values within the activation layer. Through extensive experiments and qualitative comparisons, we demonstrate that ScoreCAM++ consistently achieves notably superior performance and fairness in interpreting the decision-making process compared to both ScoreCAM and previous methods.

Recent work has shown that attention-based language models excel at recall, the ability to ground generations in tokens previously seen in context. However, the efficiency of attention-based models is bottle-necked during inference by the KV-cache's aggressive memory consumption. In this work, we explore whether we can improve language model efficiency (e.g. by reducing memory consumption) without compromising on recall. By applying experiments and theory to a broad set of architectures, we identify a key tradeoff between a model's state size and recall ability. We show that efficient alternatives to attention (e.g. H3, Mamba, RWKV) maintain a fixed-size recurrent state, but struggle at recall. We propose BASED a simple architecture combining linear and sliding window attention. By varying BASED window size and linear attention feature dimension, we can dial the state size and traverse the pareto frontier of the recall-memory tradeoff curve, recovering the full quality of attention on one end and the small state size of attention-alternatives on the other. We train language models up to 1.3b parameters and show that BASED matches the strongest sub-quadratic models (e.g. Mamba) in perplexity and outperforms them on real-world recall-intensive tasks by 6.22 accuracy points. Implementations of linear attention are often less efficient than optimized standard attention implementations. To make BASED competitive, we develop IO-aware algorithms that enable 24x higher throughput on language generation than FlashAttention-2, when generating 1024 tokens using 1.3b parameter models. Code for this work is provided at: https://github.com/HazyResearch/based.

Totally asymmetric simple exclusion process (TASEP) sets the paradigm for one-dimensional driven single file motion. We study a periodic TASEP with two ``road blocks'' or defects of different kinds, one point and another extended, across which particle flows are inhibited. We show how the interplay between particle number conservation and competition between the defects lead to inhomogeneous steady states with localised domain walls (LDW) or static density shocks, whose locations jump discontinuously, indicating a first order transition between these LDW states, as the system passes from being controlled by one defect to the other. When the defects are ``competing'', instead of an LDW a pair of delocalised domain walls are found, none of which can penetrate the extended defect. A minimum current principle can be used to identify the dominant defect that controls the domain wall formations., Comment: 10 pages, 8 figures, supplementary movies available on request

Abstractive text summarization is surging with the number of training samples to cater to the needs of the deep learning models. These models tend to exploit the training data representations to attain superior performance by improving the quantitative element of the resultant summary. However, increasing the size of the training set may not always be the ideal solution to maximize the performance, and therefore, a need to revisit the quality of training samples and the learning protocol of deep learning models is a must. In this paper, we aim to discretize the vector space of the abstractive text summarization models to understand the characteristics learned between the input embedding space and the models' encoder space. We show that deep models fail to capture the diversity of the input space. Further, the distribution of data points on the encoder space indicates that an unchecked increase in the training samples does not add value; rather, a tear-down of data samples is highly needed to make the models focus on variability and faithfulness. We employ clustering techniques to learn the diversity of a model's sample space and how data points are mapped from the embedding space to the encoder space and vice versa. Further, we devise a metric to filter out redundant data points to make the model more robust and less data hungry. We benchmark our proposed method using quantitative metrics, such as Rouge, and qualitative metrics, such as BERTScore, FEQA and Pyramid score. We also quantify the reasons that inhibit the models from learning the diversity from the varied input samples.

Attention-free language models that combine gating and convolutions are growing in popularity due to their efficiency and increasingly competitive performance. To better understand these architectures, we pretrain a suite of 17 attention and "gated-convolution" language models, finding that SoTA gated-convolution architectures still underperform attention by up to 2.1 perplexity points on the Pile. In fine-grained analysis, we find 82% of the gap is explained by each model's ability to recall information that is previously mentioned in-context, e.g. "Hakuna Matata means no worries Hakuna Matata it means no" $\rightarrow$ "??". On this task, termed "associative recall", we find that attention outperforms gated-convolutions by a large margin: a 70M parameter attention model outperforms a 1.4 billion parameter gated-convolution model on associative recall. This is surprising because prior work shows gated convolutions can perfectly solve synthetic tests for AR capability. To close the gap between synthetics and real language, we develop a new formalization of the task called multi-query associative recall (MQAR) that better reflects actual language. We perform an empirical and theoretical study of MQAR that elucidates differences in the parameter-efficiency of attention and gated-convolution recall. Informed by our analysis, we evaluate simple convolution-attention hybrids and show that hybrids with input-dependent sparse attention patterns can close 97.4% of the gap to attention, while maintaining sub-quadratic scaling. Our code is accessible at: https://github.com/HazyResearch/zoology.

We observed $\gamma$-ray burst (GRB) 221009A using very long baseline interferomety (VLBI) with the European VLBI Network (EVN) and the Very Long Baseline Array (VLBA), over a period spanning from 40 to 262 days after the initial GRB. The high angular resolution (mas) of our observations allowed us, for the second time ever, after GRB 030329, to measure the projected size, $s$, of the relativistic shock caused by the expansion of the GRB ejecta into the surrounding medium. Our observations support the expansion of the shock with a $>4\sigma$-equivalent significance, and confirm its relativistic nature by revealing an apparently superluminal expansion rate. Fitting a power law expansion model, $s\propto t^a$, to the observed size evolution, we find a slope $a=0.69^{+0.13}_{-0.14}$. Fitting the data at each frequency separately, we find different expansion rates, pointing to a frequency-dependent behaviour. We show that the observed size evolution can be reconciled with a reverse shock plus forward shock, provided that the two shocks dominate the emission at different frequencies and, possibly, at different times., Comment: Accepted version for publication

Spin glasses are canonical examples of complex matter. Although much about their structure remains uncertain, they inform the description of a wide array of complex phenomena, ranging from magnetic ordering in metals with impurities to aspects of evolution, protein folding, climate models, combinatorial optimization, and artificial intelligence. Indeed, spin glass theory forms a mathematical basis for neuromorphic computing and brain modeling. Advancing experimental insight into their structure requires repeatable control over microscopic degrees of freedom. Here, we achieve this at the atomic level using a quantum-optical system comprised of ultracold gases of atoms coupled via photons resonating within a confocal cavity. This active quantum gas microscope realizes an unusual type of transverse-field vector spin glass with all-to-all connectivity. Spin configurations are observed in cavity emission and reveal the emergence of replica symmetry breaking and nascent ultrametric structure as signatures of spin-glass order. The driven-dissipative nature of the system manifests as a nonthermal Parisi distribution, in qualitative correspondence with Monte Carlo simulations. The controllability provided by this new spin-glass system, potentially down to the quantum-spin-level, enables the study of spin-glass physics in novel regimes with application to quantum neural network computing., Comment: main text 7 pages and 4 figures, supplement 20 pages and 11 figures

The concepts of geometric phase and wave-particle duality are interlinked to several fundamental phenomena in quantum physics, but their mutual relationship still forms an uncharted open problem. Here we address this question by studying the geometric phase of a photon in double-slit interference. We especially discover a general complementarity relation for the photon that connects the geometric phase it exhibits in the observation plane and the which-path information it encases at the two slits. The relation can be seen as quantifying wave-particle duality of the photon via the geometric phase, thus corroborating a foundational link between two ubiquitous notions in quantum physics research.

Recent advances in attention-free sequence models rely on convolutions as alternatives to the attention operator at the core of Transformers. In particular, long convolution sequence models have achieved state-of-the-art performance in many domains, but incur a significant cost during auto-regressive inference workloads -- naively requiring a full pass (or caching of activations) over the input sequence for each generated token -- similarly to attention-based models. In this paper, we seek to enable $\mathcal O(1)$ compute and memory cost per token in any pre-trained long convolution architecture to reduce memory footprint and increase throughput during generation. Concretely, our methods consist in extracting low-dimensional linear state-space models from each convolution layer, building upon rational interpolation and model-order reduction techniques. We further introduce architectural improvements to convolution-based layers such as Hyena: by weight-tying the filters across channels into heads, we achieve higher pre-training quality and reduce the number of filters to be distilled. The resulting model achieves 10x higher throughput than Transformers and 1.5x higher than Hyena at 1.3B parameters, without any loss in quality after distillation.

Machine learning models are increasingly being scaled in both sequence length and model dimension to reach longer contexts and better performance. However, existing architectures such as Transformers scale quadratically along both these axes. We ask: are there performant architectures that can scale sub-quadratically along sequence length and model dimension? We introduce Monarch Mixer (M2), a new architecture that uses the same sub-quadratic primitive along both sequence length and model dimension: Monarch matrices, a simple class of expressive structured matrices that captures many linear transforms, achieves high hardware efficiency on GPUs, and scales sub-quadratically. As a proof of concept, we explore the performance of M2 in three domains: non-causal BERT-style language modeling, ViT-style image classification, and causal GPT-style language modeling. For non-causal BERT-style modeling, M2 matches BERT-base and BERT-large in downstream GLUE quality with up to 27% fewer parameters, and achieves up to 9.1$\times$ higher throughput at sequence length 4K. On ImageNet, M2 outperforms ViT-b by 1% in accuracy, with only half the parameters. Causal GPT-style models introduce a technical challenge: enforcing causality via masking introduces a quadratic bottleneck. To alleviate this bottleneck, we develop a novel theoretical view of Monarch matrices based on multivariate polynomial evaluation and interpolation, which lets us parameterize M2 to be causal while remaining sub-quadratic. Using this parameterization, M2 matches GPT-style Transformers at 360M parameters in pretraining perplexity on The PILE--showing for the first time that it may be possible to match Transformer quality without attention or MLPs., Comment: NeurIPS 2023 (Oral)

The increased attention to regulating the outputs of deep generative models, driven by growing concerns about privacy and regulatory compliance, has highlighted the need for effective control over these models. This necessity arises from instances where generative models produce outputs containing undesirable, offensive, or potentially harmful content. To tackle this challenge, the concept of machine unlearning has emerged, aiming to forget specific learned information or to erase the influence of undesired data subsets from a trained model. The objective of this work is to prevent the generation of outputs containing undesired features from a pre-trained GAN where the underlying training data set is inaccessible. Our approach is inspired by a crucial observation: the parameter space of GANs exhibits meaningful directions that can be leveraged to suppress specific undesired features. However, such directions usually result in the degradation of the quality of generated samples. Our proposed method, known as 'Adapt-then-Unlearn,' excels at unlearning such undesirable features while also maintaining the quality of generated samples. This method unfolds in two stages: in the initial stage, we adapt the pre-trained GAN using negative samples provided by the user, while in the subsequent stage, we focus on unlearning the undesired feature. During the latter phase, we train the pre-trained GAN using positive samples, incorporating a repulsion regularizer. This regularizer encourages the model's parameters to be away from the parameters associated with the adapted model from the first stage while also maintaining the quality of generated samples. To the best of our knowledge, our approach stands as first method addressing unlearning in GANs. We validate the effectiveness of our method through comprehensive experiments., Comment: 15 pages, 12 figures

The origin of the observed diffuse neutrino flux is not yet known. Studies of the relative flavour content of the neutrino flux detected at Earth can give information on the production mechanisms at the sources and on flavour mixing, complementary to measurements of the spectral index and normalisation. Here we demonstrate the effects of neutrino fluxes with different spectral shapes and different initial flavour compositions dominating at different energies, and we study the sensitivity of future measurements with the IceCube Neutrino Observatory. Where one kind of flux gives way to another, this shows up as a non-trivial energy dependence in the flavour compositions. We explore this in the context of slow-jet supernovae and magnetar-driven supernovae -- two examples of astrophysical sources where charm production may be effective. Using current best-fit neutrino mixing parameters and their projected 2040 uncertainties, we use event ratios of different event morphologies at IceCube to illustrate the possibilities of distinguishing the energy dependence of neutrino flavour ratios., Comment: v1: 20 pages, 6 figures; v2: 22 pages, 8 figures, published version

Proton auroras are widely observed on the dayside of Mars, identified as a significant intensity enhancement in the hydrogen Lyman alpha (121.6 nm) emission between 110 - 150 km altitudes. Solar wind protons penetrating as energetic neutral atoms into Mars thermosphere are thought to be primarily responsible for these auroras. Recent observations of spatially localized (patchy) proton auroras suggest a possible direct deposition of protons into Mars atmosphere during unstable solar wind conditions. Improving our understanding of proton auroras is therefore important for characterizing the solar wind interaction with Mars atmosphere. Here, we develop a first purely data-driven model of proton auroras using Mars Atmosphere and Volatile EvolutioN (MAVEN) in-situ observations and limb scans of Ly-alpha emissions between 2014 - 2022. We train an artificial neural network (ANN) that reproduces individual Lyman alpha intensities and relative Lyman alpha peak intensity enhancements with a Pearson correlation of 0.94 and 0.60 respectively for the test data, along with a faithful reconstruction of the shape of the observed Lyman alpha emission altitude profiles. By performing a SHapley Additive exPlanations (SHAP) analysis, we find that solar zenith angle, solar longitude, CO2 atmosphere variability, solar wind speed and temperature are the most important features for the modeled Lyman alpha peak intensity enhancements. Additionally, we find that the modeled peak intensity enhancements are high for early local time hours, particularly near polar latitudes, as well as weaker induced magnetic fields. Through SHAP analysis, we also identify the influence of biases in the training data and interdependecies between the measurements used for the modeling, and an improvement on those aspects can significantly improve the performance and applicability of the ANN model., Comment: 23 Pages, 17 Figures, 5 Tables, Accepted in PsJ

For the past several decades, numerous attempts have been made to model the climate of Mars with extensive studies focusing on the planet's dynamics and the understanding of its climate. While physical modeling and data assimilation approaches have made significant progress, uncertainties persist in comprehensively capturing and modeling the complexities of Martian climate. In this work, we propose a novel approach to Martian climate modeling by leveraging machine learning techniques that have shown remarkable success in Earth climate modeling. Our study presents a deep neural network designed to accurately model relative humidity in Gale Crater, as measured by NASA's Mars Science Laboratory ``Curiosity'' rover. By utilizing simulated meteorological variables produced by the Mars Planetary Climate Model, a robust Global Circulation Model, our model accurately predicts relative humidity with a mean error of 3\% and an $R^2$ score of 0.92. Furthermore, we present an approach to predict quantile ranges of relative humidity, catering to applications that require a range of values. To address the challenge of interpretability associated with machine learning models, we utilize an interpretable model architecture and conduct an in-depth analysis of its internal mechanisms and decision making processes. We find that our neural network can effectively model relative humidity at Gale crater using a few meteorological variables, with the monthly mean surface H$_2$O layer, planetary boundary layer height, convective wind speed, and solar zenith angle being the primary contributors to the model predictions. In addition to providing a fast and efficient method to modeling climate variables on Mars, this modeling approach can also be used to expand on current datasets by filling spatial and temporal gaps in observations., Comment: 13 pages, 7 figures

Using multi-frequency Very Long Baseline Interferometer (VLBI) observations, we probe the jet size in the optically thick hard state jets of two black hole X-ray binary (BHXRB) systems, MAXI J1820+070 and V404 Cygni. Due to optical depth effects, the phase referenced VLBI core positions move along the jet axis of the BHXRB in a frequency dependent manner. We use this "core shift" to constrain the physical size of the hard state jet. We place an upper limit of $0.3$\,au on the jet size measured between the 15 and 5 GHz emission regions of the jet in MAXI J1820+070, and an upper limit of $1.0$\,au between the $8.4$ and $4.8$\,GHz emission regions of V404 Cygni. Our limit on the jet size in MAXI J1820+070 observed in the low-hard state is a factor of $5$ smaller than the values previously observed in the high-luminosity hard state (using time lags between multi-frequency light curves), thus showing evidence of the BHXRB jet scaling in size with jet luminosity. We also investigate whether motion of the radio-emitting region along the jet axis could affect the measured VLBI parallaxes for the two systems, leading to a mild tension with the parallax measurements of Gaia. Having mitigated the impact of any motion along the jet axis in the measured astrometry, we find the previous VLBI parallax measurements of MAXI J1820+070 and V404 Cygni to be unaffected by jet motion. With a total time baseline of $8$ years, due to having incorporated fourteen new epochs in addition to the previously published ones, our updated parallax measurement of V404 Cygni is $0.450 \pm 0.018$\,mas ($2.226 \pm 0.091$\,kpc)., Comment: Accepted in MNRAS. 7 Figures and 3 Tables

We study the high-scale validity of two kinds of two Higgs doublet models (2HDM), namely, Type-II and Type-X, but with a scalar SU(2) singlet dark matter (DM) candidate in addition in each case. The additional quartic couplings involving the DM particle in the scalar potential in both the scenarios bring in additional constraints from the requirement of perturbative unitarity and vacuum stability. DM relic density and direct search constraints play a crucial role in this analysis as the perturbative unitarity of the DM-Higgs portal couplings primarily decide the high scale validity of the model. We find that, within the parameter regions thus restricted, the Type-II scenario must have a cut-off at around $10^6$ GeV, while the Type-X scenario admits of validity upto the Planck scale. However, only those regions which are valid upto about $10^8$ GeV in Type-X 2HDM is amenable to detection at the High-luminosity LHC (upto 3000 $fb^{-1}$), while most of the parameter space of the Type-II scenario mentioned above is likely to be detectable., Comment: 32 pages, 6 figures, 4 tables

Wormhole solutions in General Relativity (GR) require \textit{exotic} matter sources that violate the null energy condition (NEC), and it is well known that higher-order modifications of GR and some alternative matter sources can support wormholes. In this study, we explore the possibility of formulating traversable wormholes in $f(R)$ modified gravity, which is perhaps the most widely discussed modification of GR, with two approaches. First, to investigate the effects of geometrical constraints on the global characteristics, we gauge the $rr$-component of the metric tensor, and employ Pad\`{e} approximation to check whether a well-constrained \textit{shape function} can be formulated in this manner. We then derive the field equations with a background of string cloud, and numerically analyse the energy conditions, stability, and amount of exotic matter in this space-time. Next, as an alternative source in a simple $f(R)$ gravity model, we use the background cloud of strings to estimate the wormhole shape function, and analyse the relevant properties of the space-time. These results are then compared with those of wormholes threaded by normal matter in the simple $f(R)$ gravity model considered. The results demonstrate that wormholes with NEC violations are feasible; however, the wormhole space-times in the simple $f(R)$ gravity model are unstable.