A Location Privacy-Preserving Method for Spectrum Sharing in Database-Driven Cognitive Radio Networks

The great attention to cognitive radio networks (CRNs) in recent years, as a revolutionary communication paradigm that aims to solve the problem of spectrum scarcity, prompts serious investigation on security issues of these networks. One important security concern in CRNs is the preservation of users location privacy, which is under the shadow of threat, especially in database-driven CRNs. To this end, in this paper, we propose a Location Privacy Preserving Database-Driven Spectrum-Sharing \((\hbox {L-PDS}^2)\) protocol for sharing the spectrum between PUs and SUs in a database-driven CRN, while protecting location privacy of both primary and secondary users, simultaneously. We also present two specific algorithms as implementations of \(\hbox {L-PDS}^2\) protocol. Our analytical results for the privacy protection capability of \(\hbox {L-PDS}^2\) protocol prove that it provides location privacy preservation with very high probability for users of both networks. Moreover, the simulation results show that the proposed algorithms are efficient in terms of run time.     

An efficient resource management scheme in light-trail networks

Light-trail, a framework proposed in the past few years, is generalized from the concept of lightpath, and its distinguishing features include bandwidth sharing and efficient bandwidth utilization. Performance of light-trail networks depends on the routing algorithm and the dynamic bandwidth allocation (DBA) scheme, and the former issue has been discussed extensively. In this work, we aim at the design of an efficient DBA scheme, named Demand and Delay-latency Aware with Two-round Deliberation \((\hbox {D}^{2}\hbox {ATD})\), to allocate bandwidth more accurately and efficiently in light-trail networks. In addition to DBA issue, \(\hbox {D}^{2}\hbox {ATD}\) includes a light-trail setup/release mechanism as well. As expected, the simulation results reveal superiority of \(\hbox {D}^{2}\hbox {ATD}\) in both blocking performance and delay performance. Although \(\hbox {D}^{2}\hbox {ATD}\) pays a price of control overhead for performance gain, it is still reasonable since the amount of control messages does not exceed the capacity of the control channel. It verifies that \(\hbox {D}^{2}\hbox {ATD}\) can properly employ the control channel to achieve excellent performance.     

A deterministic auto-regressive STAP approach for nonhomogenerous clutter suppression

Direct data domain (DDD) space-time adaptive processing methods avoid nonhomogenerous training samples and can effectively suppress the clutter within the test range cell. However, it suffers inevitable performance loss due to the spatial and temporal smoothing process. Furthermore, the clutter suppression ability of these methods sharply degrades when applied to non-uniform and non-linear array for airborne radar. In this paper, a novel clutter suppression approach in the direct data domain is proposed, which describes clutter characteristic of the test range cell with AR model. For convenience, the novel method is referred to as \(\hbox {D}^{3}\hbox {AR}\). It utilizes the most system DOF. Hence, it suffers less aperture loss, compared to conventional DDD methods, e.g., the direct data domain least squares (\(\hbox {D}^{3}\hbox {LS}\)). More importantly, \(\hbox {D}^{3}\hbox {AR}\) can achieve much better clutter suupression prformance than \(\hbox {D}^{3}\hbox {LS}\) when applied to conformal array airborne radar because it does not need the spatial smoothing. The effectiveness of the \(\hbox {D}^{3}\hbox {AR}\) is verified by numerical examples for the case of a circular array.     

New refractive index profiles of dispersion-flattened highly nonlinear fibers for future all-optical signal processing in wdm optical networks

In this paper, we demonstrate new dissimilar refractive index profiles for highly nonlinear ultra-flattened dispersion fibers with noteworthy effective area \((A_\mathrm{eff})\) for future optical signal processing. The newly proposed fibers named from Type 1 to Type 5 have a flattened dispersion over S, C, L and U bands. Predominantly, few-mode HNL-UFF fiber of Type 3 yields dispersion-flattened characteristics over a range of 250 nm of optical communication spectrum with a mere 0.2 ps/nm km variation in dispersion and a dispersion slope of \(0.0057\hbox { ps}/\hbox {nm}^{2}\) km due to the contribution of higher-order modes to the dispersion characteristics of the fiber. Moreover, it has a moderate nonlinear coefficient of \(8.03\hbox { W}^{-1}\,\hbox {km}^{-1}\). By modifying the refractive index profile of Type 3 fiber, Type 4 and Type 5 fibers are obtained in order to ensure single-mode operation, while the zero flattened dispersion characteristics of the fiber are compromised. Among the newly proposed fibers, Type 4 fiber offers a very low ITU-T cutoff wavelength of \(1.33~\upmu \hbox {m}\), whereas in the case of Type 5 fiber it is \(1.38~\upmu \hbox {m}\). Moreover, Type 4 and Type 5 fibers have good nonlinear coefficients of \(12.26\hbox { W}^{-1}\,\hbox {km}^{-1}\) and \(11.45\hbox { W}^{-1}\,\hbox {km}^{-1}\), respectively. By virtue of the proposed optimized index profile, an insensitive behavior toward bending is displayed by Type 3, Type 4 and Type 5 fibers. In addition, Type 4 fiber provides a better splice loss of 0.25 dB.     

Study on the Effect of Mn,Zn, and Sb on Undercooling Behavior of Sn-Ag-Cu Alloys Using Differential Thermal Analysis

Differential thermal analysis (DTA) has been conducted on directionally solidified near-eutectic Sn-3.0 wt.%Ag-0.5 wt.%Cu (SAC), SAC \(+\) 0.2 wt.%Sb, SAC \(+\) 0.2 wt.%Mn, and SAC \(+\) 0.2 wt.%Zn. Laser ablation inductively coupled plasma mass spectroscopy was used to study element partitioning behavior and estimate DTA sample compositions. Mn and Zn additives reduced the undercooling of SAC from 20.4\(^\circ \hbox {C}\) to \(4.9^\circ \hbox {C}\) and \(2^\circ \hbox {C}\), respectively. Measurements were performed at cooling rate of \(10^\circ \hbox {C}\) per minute. After introducing 200 ppm \(\hbox {O}_2\) into the DTA, this undercooling reduction ceased for SAC \(+\) Mn but persisted for SAC \(+\) Zn.     

Application of photonic crystal ring resonator nonlinear response for full-optical tunable add–drop filtering

In this paper, we investigate the application of Kerr-like nonlinear photonic crystal (PhC) ring resonator (PCRR) for realizing a tunable full-optical add–drop filter. We used silicon (Si) nano-crystal as the nonlinear material in pillar-based square lattice of a 2DPhC. The nonlinear section of PCRR is studied under three different scenarios: (1) first only the inner rods of PCRR are made of nonlinear materials, (2) only outer rods of PCRR have nonlinear response, and (3) both of inner and outer rods are made of nonlinear material. The simulation results indicate that optical power required to switch the state of PCRR from turn-on to turn-off, for the nonlinearity applied to inner PCRR, is at least \(2000\, \hbox {mW}{/}\upmu \hbox {m}^{2}\) and, for the nonlinearity applied to outer PCRR, is at least \(3000\, \hbox {mW}{/}\upmu \hbox {m}^{2}\) which corresponds to refractive index change of \(\Delta n_\mathrm{NL }= 0.085\) and \(\Delta n_\mathrm{NL }= 0.15\), respectively. For nonlinear tuning of add–drop filter, the minimum power required to 1 nm redshift the center operating wavelength \((\lambda _{0} = 1550\, \hbox {nm})\) for the inner PCRR scenario is \(125\, \hbox {mW}{/}\upmu \hbox {m}^{2}\) (refractive index change of \(\Delta n_\mathrm{NL}= 0.005)\). Maximum allowed refractive index change for inner and outer scenarios before switch goes to saturation is \(\Delta n_\mathrm{NL }= 0.04\) (maximum tune-ability 8 nm) and \(\Delta n_\mathrm{NL }= 0.012\) (maximum tune-ability of 24 nm), respectively. Performance of add–drop filter is replicated by means of finite-difference time-domain method, and simulations displayed an ultra-compact size device with ultra-fast tune-ability speed.     

A 3.1–10.6 GHz UWB LNA Based on Self Cascode Technique for Improved Bandwidth and High Gain

In this work, we present a self cascode based ultra-wide band (UWB) low noise amplifier (LNA) with improved bandwidth and gain for 3.1–10.6 GHz wireless applications. The self cascode (SC) or split-length compensation technique is employed to improve the bandwidth and gain of the proposed LNA. The improvement in the bandwidth of SC based structure is around 1.22 GHz as compared to simple one. The significant enhancement in the characteristics of the introduced circuit is found without extra passive components. The SC based CS–CG structure in the proposed LNA uses the same DC current for operating first stage transistors. In the designed UWB LNA, a common source (CS) stage is used in the second stage to enhance the overall gain in the high frequency regime. With a standard 90 nm CMOS technology, the presented UWB LNA results in a gain \(\hbox {S}_{21}\) of \(20.10 \pm 1.65\,\hbox {dB}\) across the 3.1–10.6 GHz frequency range, and dissipating 11.52 mW power from a 1 V supply voltage. However, input reflection, \(\hbox {S}_{11}\), lies below \(-\,10\) dB from 4.9–9.1 GHz frequency. Moreover, the output reflection (\(\hbox {S}_{22}\)) and reverse isolation (\(\hbox {S}_{12}\)), is below \(-\,10\) and \(-\,48\) dB, respectively for the ultra-wide band region. Apart from this, the minimum noise figure (\(\hbox {NF}_{min}\)) value of the proposed UWB LNA exists in the range of 2.1–3 dB for 3.1–10.6 GHz frequency range with a a small variation of \(\pm \,0.45\,\hbox {dB}\) in its \(\hbox {NF}_{min}\) characteristics. Linearity of the designed LNA is analysed in terms of third order input intercept point (IIP3) whose value is \(-\,4.22\) dBm, when a two tone signal is applied at 6 GHz with a spacing of 10 MHz. The other important benefits of the proposed circuit are its group-delay variation and gain variation of \(\pm \,115\,\hbox {ps}\) and \(\pm \,1.65\,\hbox {dB}\), respectively.     

Electrical Transport Mechanisms and Photoconduction in Undoped Crystalline Flash-Evaporated Lead Iodide Thin Films

The flash-evaporation technique was utilized to fabricate undoped 1.35-μm and 1.2-μm thick lead iodide films at substrate temperatures \( T_{\rm{s}} = 150 \)°C and 200°C, respectively. The films were deposited onto a coplanar comb-like copper (Cu-) electrode pattern, previously coated on glass substrates to form lateral metal–semiconductor–metal (MSM-) structures. The as-measured constant-temperature direct-current (dc)-voltage (\( I\left( {V;T} \right) - V \)) curves of the obtained lateral coplanar Cu-PbI₂-Cu samples (film plus electrode) displayed remarkable ohmic behavior at all temperatures (\( T = 18 - 90\,^\circ {\hbox{C}} \)). Their dc electrical resistance \( R_{\rm{dc}} (T \)) revealed a single thermally-activated conduction mechanism over the temperature range with activation energy \( E_{\rm{act}} \approx 0.90 - 0.98 \,{\hbox{eV}} \), slightly less than half of room-temperature bandgap energy \( E_{\rm{g}} \) (\( \approx \,2.3\, {\hbox{eV}} \)) of undoped 2H-polytype PbI₂ single crystals. The undoped flash-evaporated \( {\hbox{PbI}}_{\rm{x}} \) thin films were homogeneous and almost stoichiometric (\( x \approx 1.87 \)), in contrast to findings on lead iodide films prepared by other methods, and were highly crystalline hexagonal 2H-polytypic structure with c-axis perpendicular to the surface of substrates maintained at \( T_{\rm{s}} { \gtrsim }150^\circ {\hbox{C}} \). Photoconductivity measurements made on these lateral Cu-PbI₂-Cu-structures under on–off visible-light illumination reveal a feeble photoresponse for long wavelengths (\( \lambda > 570\,{\hbox{nm}} \)), but a strong response to blue light of photon energy \( E_{\rm{ph}} \) \( \approx \,2.73 \, {\hbox{eV}} \) (\( > E_{\rm{g}} \)), due to photogenerated electron–hole (e–h) pairs via direct band-to-band electronic transitions. The constant-temperature/dc voltage current–time \( I\left( {T,V} \right) - t \) curves of the studied lateral PbI₂ MSM-structures at low ambient temperatures (\( T < 50^\circ {\hbox{C}} \)), after cutting off the blue-light illumination, exhibit two trapping mechanisms with different relaxation times. These strongly depend on \( V \) and \( T \), with thermally generated charge carriers in the PbI₂ mask photogenerated (e–h) pairs at higher temperatures.     

A Low-Voltage Fully Differential Pure Current Mode Current Operational Amplifier

In this paper a novel high-frequency fully differential pure current mode current operational amplifier (COA) is proposed that is, to the authors’ knowledge, the first pure MOSFET Current Mode Logic (MCML) COA in the world, so far. Doing fully current mode signal processing and avoiding high impedance nodes in the signal path grant the proposed COA such outstanding properties as high current gain, broad bandwidth, and low voltage and low-power consumption. The principle operation of the block is discussed and its outstanding properties are verified by HSPICE simulations using TSMC \(0.18\,\upmu \hbox {m}\) CMOS technology parameters. Pre-layout and Post-layout both plus Monte Carlo simulations are performed under supply voltages of \(\pm 0.75\,\hbox {V}\) to investigate its robust performance at the presence of fabrication non-idealities. The pre-layout plus Monte Carlo results are as; 93 dB current gain, \(8.2\,\hbox {MHz}\,\, f_{-3\,\text {dB}}, 89^{\circ }\) phase margin, 137 dB CMRR, 13 \(\Omega \) input impedance, \(89\,\hbox {M}\Omega \) output impedance and 1.37 mW consumed power. Also post-layout plus Monte Carlo simulation results (that are generally believed to be as reliable and practical as are measuring ones) are extracted that favorably show(in abovementioned order of pre-layout) 88 dB current gain, \(6.9\,\hbox {MHz} f_{-3\text {db}} , 131^{\circ }\) phase margin and 96 dB CMRR, \(22\,\Omega \) input impedance, \(33\,\hbox {M}\Omega \) output impedance and only 1.43 mW consumed power. These results altogether prove both excellent quality and well resistance of the proposed COA against technology and fabrication non-idealities.     

Study on Time Domain Characteristics of Memristive RLC Series Circuits

The notion of memristive system was first proposed in 2009. This concept of memory element has been extended from memristors \((\hbox {R}_{\mathrm{M}})\) to memcapacitors \((\hbox {C}_{\mathrm{M}})\) and meminductors \((\hbox {L}_{\mathrm{M}})\). Currently, the above elements are not available as off-the-shelf components. Therefore, based on the realization of a light-dependent resistor (LDR), memristor analog model, memcapacitor and meminductor analog circuit models based on \(\hbox {R}_{\mathrm{M}}-\hbox {C}_{\mathrm{M}}\) and \(\hbox {R}_{\mathrm{M}}-\hbox {L}_{\mathrm{M}}\) converters are first introduced. Then, instead of the traditional resistor, capacitor, and inductor, memristor-, memcapacitor-, and meminductor-equivalent circuits are used to determine the time domain characteristics of the RLC-mode circuits with mem-elements. These circuits are discussed in detail, and in particular, the phenomena caused by the memory characteristics of the mem-elements are studied. This research provides an important reference for further research into mem-element applications in circuit theory.     

Modeling and analysis of red emission in $$\hbox {Pr}^{3+}$$-doped fiber lasers

In order to improve the performance of the \(\hbox {Pr}^{3+}\)-doped fiber laser, the optimum fiber length and reflectivity of mirrors, the maximum output power, the lasing threshold, and the slope efficiency are needed to be estimated. In this work, a \(\hbox {Pr}^{3+}\)-doped fiber laser is considered with fiber Bragg gratings (FBG) as reflectors and an injected pump power in one side. To do so, the rate and power propagation equations of the \(\hbox {Pr}^{3+}\)-doped fiber laser are solved numerically by finite difference method and the boundary conditions are obtained by shooting method in an iterative process. The effect of some structural parameters such as the laser background loss, the pump power, the \(\hbox {Pr}^{3+}\) dopant concentration, and the reflectivity coefficient of FBG2 on the performance of laser is studied, and the optimum values for fiber length and reflectivity of FBG2 are obtained.     

Correction to: A subthreshold low-power CMOS LC-VCO with high immunity to PVT variations

This paper presents a capacitor-free low dropout (LDO) linear regulator based on a dual loop topology. The regulator utilizes two feedback loops to satisfy the challenges of hearing aid devices, which include fast transient performance and small voltage spikes under rapid load-current changes. The proposed design works without the need of a decoupling capacitor connected at the output and operates with a 0–100 pF capacitive load. The design has been taped out in a \(0.18\,\upmu \hbox {m}\) CMOS process. The proposed regulator has a low component count, area of \(0.012\, \hbox {mm}^2\) and is suitable for system-on-chip integration. It regulates the output voltage at 0.9 V from a 1.0–1.4 V supply. The measured results for a current step load from 250 to 500 \(\upmu \hbox {A}\) with a rise and fall time of \(1.5\,\upmu \hbox {s}\) are an overshoot of 26 mV and undershoot of 26 mV with a settling time of \(3.5\,\upmu \hbox {s}\) when \({C_L}\) between 0 and 100 pF. The proposed LDO regulator consumes a quiescent current of only \(10.5\,\upmu \hbox {A}\). The design is suitable for application with a current step edge time of 1 ns while maintaining \(\Delta V_{out}\) of 64 mV.     

On the ratio of independent complex Gaussian random variables

In this paper, we derive a closed form equation for the joint probability distribution \({{f_{{R}_{z}}},{\varTheta _{z}}}({r_{z}},{\theta _{z}})\) of the amplitude \({R_{z}}\) and phase \({\varTheta _{z}}\) of the ratio \({Z=\frac{X}{Y}}\) of two independent non-zero mean Complex Gaussian random variables \(X\sim CN(\nu _{x} \mathrm {e}^{j\phi _{x}},{\sigma ^{2}_{x}})\) and \(Y\sim CN(\nu _{y} \mathrm {e}^{j\phi _{y}},{\sigma ^{2}_{y}})\). The derived joint probability distribution only contains a confluent hypergeometric function of the first kind \({_1F_{1}}\) without infinite summations resulting in computational efficiency. We further derive the probability distribution for the ratio of two non-zero mean independent real Rician random variables containing an infinite summation generated by the estimation of the Cauchy product of equivalent series of two modified Bessel functions.     

An energy optimization in wireless sensor networks by using genetic algorithm

Wireless sensor networks (WSNs) are used for several commercial and military applications, by collecting, processing and distributing a wide range of data. Maximizing the battery life of WSNs is crucial in improving the performance of WSN. In the present study, different variations of genetic algorithm (GA) method have been implemented independently on energy models for data communication of WSNs with the objective to find out the optimal energy \(\hbox {(E)}\) consumption conditions. Each of the GA methods results in an optimal set of parameters for minimum energy consumption in WSN related to the type of selected energy model for data communication, while the best performance of the GA method [energy consumption \((\hbox {E}=3.49\times 10^{-4}\,\hbox {J})\)] is obtained in WSN for communication distance (d) \({\ge }87\,\hbox {m}\) in between the sensor cluster head and a base station.     

A novel semisupervised support vector machine classifier based on active learning and context information

This paper proposes a novel semisupervised support vector machine classifier \((\hbox {S}^{3}\hbox {VM})\) based on active learning (AL) and context information to solve the problem where the number of labeled samples is insufficient. Firstly, a new semisupervised learning method is designed using AL to select unlabeled samples as the semilabled samples, then the context information is exploited to further expand the selected samples and relabel them, along with the labeled samples train \(\hbox {S}^{3}\hbox {VM}\) classifier. Next, a new query function is designed to enhance the reliability of the classification results by using the Euclidean distance between the samples. Finally, in order to enhance the robustness of the proposed algorithm, a fusion method is designed. Several experiments on change detection are performed by considering some real remote sensing images. The results show that the proposed algorithm in comparison with other algorithms can significantly improve the detection accuracy and achieve a fast convergence in addition to verify the effectiveness of the fusion method developed in this paper.     

Stream Ciphers: A Practical Solution for Efficient Homomorphic-Ciphertext Compression

In typical applications of homomorphic encryption, the first step consists for Alice of encrypting some plaintext m under Bob’s public key \(\mathsf {pk}\) and of sending the ciphertext \(c = \mathsf {HE}_{\mathsf {pk}}(m)\) to some third-party evaluator Charlie. This paper specifically considers that first step, i.e., the problem of transmitting c as efficiently as possible from Alice to Charlie. As others suggested before, a form of compression is achieved using hybrid encryption. Given a symmetric encryption scheme \(\mathsf {E}\), Alice picks a random key k and sends a much smaller ciphertext \(c' = (\mathsf {HE}_{\mathsf {pk}}(k), \mathsf {E}_k(m))\) that Charlie decompresses homomorphically into the original c using a decryption circuit \(\mathcal {C}_{{\mathsf {E}^{-1}}}\). In this paper, we revisit that paradigm in light of its concrete implementation constraints, in particular \(\mathsf {E}\) is chosen to be an additive IV-based stream cipher. We investigate the performances offered in this context by Trivium, which belongs to the eSTREAM portfolio, and we also propose a variant with 128-bit security: Kreyvium. We show that Trivium, whose security has been firmly established for over a decade, and the new variant Kreyvium has excellent performance. We also describe a second construction, based on exponentiation in binary fields, which is impractical but sets the lowest depth record to \(8\) for \(128\)-bit security.     

Performance Analysis of a Low Profile Hybrid Antenna for Broadband Applications

In this paper, a low profile dielectric resonator antenna (DRA) is proposed and investigated. To achieve the broad impedance bandwidth the proposed antenna geometry combines the dielectric resonator antenna and an underlying microstrip-fed slot with a narrow rectangular notch, which effectively broadens the impedance bandwidth by merging the resonances of slot and DRA. The physical insight gained by the detailed parametric study has led to find out a set of guidelines for designing the antennas for any particular frequency band. The design guidelines have been verified by simulating a set of antennas designed for different frequency bands. For validation, a prototype antenna is fabricated and tested experimentally. The measured results show that the proposed DRA offers an impedance bandwidth of about \(125.34\%\) from 1.17 to 5.1 GHz with reasonable gain between 3.5 and 5.7 dBi. The volume of the proposed DRA is \(0.16\lambda _{dr}^{3}\), where \(\lambda _{dr}\) is the wavelength at center operating frequency of the DR. A comprehensive study on bandwidth shows that the proposed DRA provides maximum bandwidth in terms of the DR volume (\(\hbox {BW}/V_{dr}\)) and the DR height (\(\hbox {BW}/h_{dr}\)) than the other similar reported work on hybrid wideband DRA designs.     

Key-Recovery Attacks on <Emphasis FontCategory="SansSerif">ASASA</Emphasis>

The \(\mathsf {ASASA}\) construction is a new design scheme introduced at Asiacrypt 2014 by Biryukov, Bouillaguet and Khovratovich. Its versatility was illustrated by building two public-key encryption schemes, a secret-key scheme, as well as super S-box subcomponents of a white-box scheme. However, one of the two public-key cryptosystems was recently broken at Crypto 2015 by Gilbert, Plût and Treger. As our main contribution, we propose a new algebraic key-recovery attack able to break at once the secret-key scheme as well as the remaining public-key scheme, in time complexity \(2^{63}\) and \(2^{39}\), respectively (the security parameter is 128 bits in both cases). Furthermore, we present a second attack of independent interest on the same public-key scheme, which heuristically reduces the problem of breaking the scheme to an \(\mathsf {LPN}\) instance with tractable parameters. This allows key recovery in time complexity \(2^{56}\). Finally, as a side result, we outline a very efficient heuristic attack on the white-box scheme, which breaks instances claiming 64 bits of security under one minute on a laptop computer.     

An Accurate Performance Analysis for Regenerative Multi-hop Relaying in Wireless Networks Over Composite Multipath/Shadowed Fading

This paper presents and evaluates the performance of wireless networks that utilize the decode-and-forward relay. This multi-hop relaying scheme communicates over Extended Generalized-\({\mathcal {K}}\) (\(\hbox {EG}{\mathcal {K}}\)) composite fading channels to create performance evaluation. To this effect, new exact and easy to compute formulas for several performance metrics are derived. More specifically, new and exact-form mathematical formulas are derived for the cumulative distribution function, the generalized moments of the overall end-to-end signal-to-noise ratio, the outage probability (\({\hbox {P}}_{\text{out}}\)), the ergodic capacity (\({\mathcal {C}}_{\text{Ergodic}}\)), the moment generating function, and the average error probability (\({\hbox {Pr(e)}}\)) for different modulation schemes. Moreover, we carried out a series of computer simulation experiments in order to testify the accuracy of the derived framework. Finally, we discussed the impact of different parameters including fading/shadowing parameters, transmitted power and the number of hops on the derived expressions.